Daily Papers

We propose Quantum-informed Tensor Adaptation (QuanTA), a novel, easy-to-implement, fine-tuning method with no inference overhead for large-scale pre-trained language models. By leveraging quantum-inspired methods derived from quantum circuit structures, QuanTA enables efficient high-rank fine-tuning, surpassing the limitations of Low-Rank Adaptation (LoRA)--low-rank approximation may fail for complicated downstream tasks. Our approach is theoretically supported by the universality theorem and the rank representation theorem to achieve efficient high-rank adaptations. Experiments demonstrate that QuanTA significantly enhances commonsense reasoning, arithmetic reasoning, and scalability compared to traditional methods. Furthermore, QuanTA shows superior performance with fewer trainable parameters compared to other approaches and can be designed to integrate with existing fine-tuning algorithms for further improvement, providing a scalable and efficient solution for fine-tuning large language models and advancing state-of-the-art in natural language processing.

Despite the rapid advancement of large language models (LLMs), low-resource languages remain largely excluded from the NLP landscape. We present PunGPT2, the first fully open-source suite of Punjabi large language models, trained from scratch on a 35GB domain-diverse corpus encompassing literature, religious texts, news, and social discourse. Unlike prior multilingual approaches, PunGPT2 captures rich syntactic and morphological features unique to Punjabi through a tokenizer optimised with byte pair encoding and linguistically aligned pretraining objectives. To improve factual grounding and domain recall, we introduce Pun-RAG, a retrieval-augmented generation framework combining PunGPT2 with a dense FAISS retriever over a curated Punjabi knowledge base. We further develop Pun-Instruct, a parameter-efficient, instruction-tuned variant using QLoRA, enabling robust zero-shot and instruction-following performance with significantly reduced compute needs. As a key innovation, we propose Quantum-RAG, a novel hybrid retrieval system that fuses sparse (BM25) and dense methods with quantum-inspired semantic matching. By encoding queries using amplitude-based embeddings and retrieving via quantum kernel similarity, Quantum-RAG achieves improved contextual relevance with minimal memory overhead marking the first practical integration of quantum representations in low-resource language generation. Our models significantly outperform strong multilingual baselines (mBERT, mT5, MuRIL) in perplexity, factuality, and fluency. This work provides a scalable, reproducible blueprint for extending LLM capabilities to underrepresented languages and pioneers quantum-aware retrieval in low-resource NLP

The Quantum-Inspired Stacked Integrated Concept Graph Model (QISICGM) is an innovative machine learning framework that harnesses quantum-inspired techniques to predict diabetes risk with exceptional accuracy and efficiency. Utilizing the PIMA Indians Diabetes dataset augmented with 2,000 synthetic samples to mitigate class imbalance (total: 2,768 samples, 1,949 positives), QISICGM integrates a self-improving concept graph with a stacked ensemble comprising Random Forests (RF), Extra Trees (ET), transformers, convolutional neural networks (CNNs), and feed-forward neural networks (FFNNs). This approach achieves an out-of-fold (OOF) F1 score of 0.8933 and an AUC of 0.8699, outperforming traditional methods. Quantum inspired elements, such as phase feature mapping and neighborhood sequence modeling, enrich feature representations, enabling CPU-efficient inference at 8.5 rows per second. This paper presents a detailed architecture, theoretical foundations, code insights, and performance evaluations, including visualizations from the outputs subfolder. The open-source implementation (v1.0.0) is available at https://github.com/keninayoung/QISICGM, positioning QISICGM as a potential benchmark for AI-assisted clinical triage in diabetes and beyond. Ultimately, this work emphasizes trustworthy AI through calibration, interpretability, and open-source reproducibility.

Molecular docking is an important tool for structure-based drug design, accelerating the efficiency of drug development. Complex and dynamic binding processes between proteins and small molecules require searching and sampling over a wide spatial range. Traditional docking by searching for possible binding sites and conformations is computationally complex and results poorly under blind docking. Quantum-inspired algorithms combining quantum properties and annealing show great advantages in solving combinatorial optimization problems. Inspired by this, we achieve an improved in blind docking by using quantum-inspired combined with gradients learned by deep learning in the encoded molecular space. Numerical simulation shows that our method outperforms traditional docking algorithms and deep learning-based algorithms over 10\%. Compared to the current state-of-the-art deep learning-based docking algorithm DiffDock, the success rate of Top-1 (RMSD<2) achieves an improvement from 33\% to 35\% in our same setup. In particular, a 6\% improvement is realized in the high-precision region(RMSD<1) on molecules data unseen in DiffDock, which demonstrates the well-generalized of our method.

Large Language Models (LLMs) such as ChatGPT and LlaMA are advancing rapidly in generative Artificial Intelligence (AI), but their immense size poses significant challenges, such as huge training and inference costs, substantial energy demands, and limitations for on-site deployment. Traditional compression methods such as pruning, distillation, and low-rank approximation focus on reducing the effective number of neurons in the network, while quantization focuses on reducing the numerical precision of individual weights to reduce the model size while keeping the number of neurons fixed. While these compression methods have been relatively successful in practice, there is no compelling reason to believe that truncating the number of neurons is an optimal strategy. In this context, this paper introduces CompactifAI, an innovative LLM compression approach using quantum-inspired Tensor Networks that focuses on the model's correlation space instead, allowing for a more controlled, refined and interpretable model compression. Our method is versatile and can be implemented with - or on top of - other compression techniques. As a benchmark, we demonstrate that a combination of CompactifAI with quantization allows to reduce a 93% the memory size of LlaMA 7B, reducing also 70% the number of parameters, accelerating 50% the training and 25% the inference times of the model, and just with a small accuracy drop of 2% - 3%, going much beyond of what is achievable today by other compression techniques. Our methods also allow to perform a refined layer sensitivity profiling, showing that deeper layers tend to be more suitable for tensor network compression, which is compatible with recent observations on the ineffectiveness of those layers for LLM performance. Our results imply that standard LLMs are, in fact, heavily overparametrized, and do not need to be large at all.

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.

We analyze the DP (differential privacy) properties of the quantum recommendation algorithm and the quantum-inspired-classical recommendation algorithm. We discover that the quantum recommendation algorithm is a privacy curating mechanism on its own, requiring no external noise, which is different from traditional differential privacy mechanisms. In our analysis, a novel perturbation method tailored for SVD (singular value decomposition) and low-rank matrix approximation problems is introduced. Using the perturbation method and random matrix theory, we are able to derive that both the quantum and quantum-inspired-classical algorithms are big(mathcal{O}big(frac 1nbig),,, mathcal{O}big(1{min{m,n}}big)big)-DP under some reasonable restrictions, where m and n are numbers of users and products in the input preference database respectively. Nevertheless, a comparison shows that the quantum algorithm has better privacy preserving potential than the classical one.

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an Ntimes N matrix M, an N-dimensional vector emph{b}, and an initial vector emph{x}(0), obtain a target vector emph{x}(t) as a function of time t according to the constraint demph{x}(t)/dt=Memph{x}(t)+emph{b}. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4times4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

We propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to directly generate quantum states. We present both a full quantum and a latent quantum version of the algorithm; we also present a conditioned version of these models. The models' performances have been evaluated using quantitative metrics complemented by qualitative assessments. An implementation of a simplified version of the algorithm has been executed on real NISQ quantum hardware.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match -- at little additional computational cost -- full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

We present QuantumLLMInstruct (QLMMI), an innovative dataset featuring over 500,000 meticulously curated instruction-following problem-solution pairs designed specifically for quantum computing - the largest and most comprehensive dataset of its kind. Originating from over 90 primary seed domains and encompassing hundreds of subdomains autonomously generated by LLMs, QLMMI marks a transformative step in the diversity and richness of quantum computing datasets. Designed for instruction fine-tuning, QLMMI seeks to significantly improve LLM performance in addressing complex quantum computing challenges across a wide range of quantum physics topics. While Large Language Models (LLMs) have propelled advancements in computational science with datasets like Omni-MATH and OpenMathInstruct, these primarily target Olympiad-level mathematics, leaving quantum computing largely unexplored. The creation of QLMMI follows a rigorous four-stage methodology. Initially, foundational problems are developed using predefined templates, focusing on critical areas such as synthetic Hamiltonians, QASM code generation, Jordan-Wigner transformations, and Trotter-Suzuki quantum circuit decompositions. Next, detailed and domain-specific solutions are crafted to ensure accuracy and relevance. In the third stage, the dataset is enriched through advanced reasoning techniques, including Chain-of-Thought (CoT) and Task-Oriented Reasoning and Action (ToRA), which enhance problem-solution diversity while adhering to strict mathematical standards. Lastly, a zero-shot Judge LLM performs self-assessments to validate the dataset's quality and reliability, minimizing human oversight requirements.

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows that, given access to error-free, efficient quantum realizations of the agent and environment, quantum methods can yield provable improvements over classical Monte-Carlo based methods in terms of sample complexity. Our approach shows in detail how to combine amplitude estimation and Grover search into a policy evaluation and improvement scheme. We first develop quantum policy evaluation (QPE) which is quadratically more efficient compared to an analogous classical Monte Carlo estimation and is based on a quantum mechanical realization of a finite Markov decision process (MDP). Building on QPE, we derive a quantum policy iteration that repeatedly improves an initial policy using Grover search until the optimum is reached. Finally, we present an implementation of our algorithm for a two-armed bandit MDP which we then simulate.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the ``quantisation" of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning [1]. Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models [2]. In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit [3] with the quantum Hamiltonian data embedding unitary [4]. Through numerical experiments on images datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN)[5] by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks.

While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant computational problems remains a challenge. Proposals for attaining practical quantum advantage typically involve parametrized quantum circuits (PQCs), whose parameters can be optimized to find solutions to diverse problems throughout quantum simulation and machine learning. However, training PQCs for real-world problems remains a significant practical challenge, largely due to the phenomenon of barren plateaus in the optimization landscapes of randomly-initialized quantum circuits. In this work, we introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for PQCs, which we show significantly improves the trainability and performance of PQCs on a variety of problems. Given a specific optimization task, this method first utilizes tensor network (TN) simulations to identify a promising quantum state, which is then converted into gate parameters of a PQC by means of a high-performance decomposition procedure. We show that this learned initialization avoids barren plateaus, and effectively translates increases in classical resources to enhanced performance and speed in training quantum circuits. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing, and opens up new avenues to harness the power of modern quantum hardware for realizing practical quantum advantage.

In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.

We introduce the framework of model space into quantum imaginary time evolution (QITE) to enable stable estimation of ground and excited states using a quantum computer. Model-space QITE (MSQITE) propagates a model space to the exact one by retaining its orthogonality, and hence is able to describe multiple states simultaneously. The quantum Lanczos (QLanczos) algorithm is extended to MSQITE to accelerate the convergence. The present scheme is found to outperform both the standard QLanczos and the recently proposed folded-spectrum QITE in simulating excited states. Moreover, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. We also investigate how different levels of the unitary approximation employed in MSQITE can affect the results. The effectiveness of the algorithm over QITE is demonstrated by noise simulations for the H4 model system.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

This paper introduces the Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model for generating quantum state ensembles, inspired by Denoising Diffusion Probabilistic Models. QGDM features a diffusion process that introduces timestep-dependent noise into quantum states, paired with a denoising mechanism trained to reverse this contamination. This model efficiently evolves a completely mixed state into a target quantum state post-training. Our comparative analysis with Quantum Generative Adversarial Networks demonstrates QGDM's superiority, with fidelity metrics exceeding 0.99 in numerical simulations involving up to 4 qubits. Additionally, we present a Resource-Efficient version of QGDM (RE-QGDM), which minimizes the need for auxiliary qubits while maintaining impressive generative capabilities for tasks involving up to 8 qubits. These results showcase the proposed models' potential for tackling challenging quantum generation problems.

Quantum computation is an emerging technology with important potential for solving certain problems pivotal in various scientific and engineering disciplines. This paper introduces an efficient quantum protocol for the explicit construction of the block-encoding for an important class of Hamiltonians. Using the Schrodingerisation technique -- which converts non-conservative PDEs into conservative ones -- this particular class of Hamiltonians is shown to be sufficient for simulating any linear partial differential equations that have coefficients which are polynomial functions. The class of Hamiltonians consist of discretisations of polynomial products and sums of position and momentum operators. This construction is explicit and leverages minimal one- and two-qubit operations. The explicit construction of this block-encoding forms a fundamental building block for constructing the unitary evolution operator for this Hamiltonian. The proposed algorithm exhibits polynomial scaling with respect to the spatial partitioning size, suggesting an exponential speedup over classical finite-difference methods. This work provides an important foundation for building explicit and efficient quantum circuits for solving partial differential equations.

Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are unconstrained (such as Max-Cut). In this study, we investigate a hybrid quantum-classical method for constrained optimization problems, particularly those with knapsack constraints that occur frequently in financial and supply chain applications. Our proposed method relies firstly on relaxations to local quantum Hamiltonians, defined through commutative maps. Drawing inspiration from quantum random access code (QRAC) concepts, particularly Quantum Random Access Optimizer (QRAO), we explore QRAO's potential in solving large constrained optimization problems. We employ classical techniques like Linear Relaxation as a presolve mechanism to handle constraints and cope further with scalability. We compare our approach with QAOA and present the final results for a real-world procurement optimization problem: a significant sized multi-knapsack-constrained problem.

We investigate the potential of bio-inspired evolutionary algorithms for designing quantum circuits with specific goals, focusing on two particular tasks. The first one is motivated by the ideas of Artificial Life that are used to reproduce stochastic cellular automata with given rules. We test the robustness of quantum implementations of the cellular automata for different numbers of quantum gates The second task deals with the sampling of quantum circuits that generate highly entangled quantum states, which constitute an important resource for quantum computing. In particular, an evolutionary algorithm is employed to optimize circuits with respect to a fitness function defined with the Mayer-Wallach entanglement measure. We demonstrate that, by balancing the mutation rate between exploration and exploitation, we can find entangling quantum circuits for up to five qubits. We also discuss the trade-off between the number of gates in quantum circuits and the computational costs of finding the gate arrangements leading to a strongly entangled state. Our findings provide additional insight into the trade-off between the complexity of a circuit and its performance, which is an important factor in the design of quantum circuits.

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gily\'en, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

Multi-model fitting (MMF) presents a significant challenge in Computer Vision, particularly due to its combinatorial nature. While recent advancements in quantum computing offer promise for addressing NP-hard problems, existing quantum-based approaches for model fitting are either limited to a single model or consider multi-model scenarios within outlier-free datasets. This paper introduces a novel approach, the robust quantum multi-model fitting (R-QuMF) algorithm, designed to handle outliers effectively. Our method leverages the intrinsic capabilities of quantum hardware to tackle combinatorial challenges inherent in MMF tasks, and it does not require prior knowledge of the exact number of models, thereby enhancing its practical applicability. By formulating the problem as a maximum set coverage task for adiabatic quantum computers (AQC), R-QuMF outperforms existing quantum techniques, demonstrating superior performance across various synthetic and real-world 3D datasets. Our findings underscore the potential of quantum computing in addressing the complexities of MMF, especially in real-world scenarios with noisy and outlier-prone data.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

We introduce a robust, error-tolerant adaptive training algorithm for generalized learning paradigms in high-dimensional superposed quantum networks, or adaptive quantum networks. The formalized procedure applies standard backpropagation training across a coherent ensemble of discrete topological configurations of individual neural networks, each of which is formally merged into appropriate linear superposition within a predefined, decoherence-free subspace. Quantum parallelism facilitates simultaneous training and revision of the system within this coherent state space, resulting in accelerated convergence to a stable network attractor under consequent iteration of the implemented backpropagation algorithm. Parallel evolution of linear superposed networks incorporating backpropagation training provides quantitative, numerical indications for optimization of both single-neuron activation functions and optimal reconfiguration of whole-network quantum structure.

This concept paper aims to provide a brief outline of quantum computers, explore existing methods of quantum image classification techniques, so focusing on remote sensing applications, and discuss the bottlenecks of performing these algorithms on currently available open source platforms. Initial results demonstrate feasibility. Next steps include expanding the size of the quantum hidden layer and increasing the variety of output image options.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.

Artificial Intelligence (AI), with its multiplier effect and wide applications in multiple areas, could potentially be an important application of quantum computing. Since modern AI systems are often built on neural networks, the design of quantum neural networks becomes a key challenge in integrating quantum computing into AI. To provide a more fine-grained characterisation of the impact of quantum components on the performance of neural networks, we propose a framework where classical neural network layers are gradually replaced by quantum layers that have the same type of input and output while keeping the flow of information between layers unchanged, different from most current research in quantum neural network, which favours an end-to-end quantum model. We start with a simple three-layer classical neural network without any normalisation layers or activation functions, and gradually change the classical layers to the corresponding quantum versions. We conduct numerical experiments on image classification datasets such as the MNIST, FashionMNIST and CIFAR-10 datasets to demonstrate the change of performance brought by the systematic introduction of quantum components. Through this framework, our research sheds new light on the design of future quantum neural network models where it could be more favourable to search for methods and frameworks that harness the advantages from both the classical and quantum worlds.

Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability is still lacking. In this work, we introduce a comprehensive benchmarking framework designed to systematically evaluate a range of quantum optimization techniques against well-established NP-hard combinatorial problems. Our framework focuses on key problem classes, including the Multi-Dimensional Knapsack Problem (MDKP), Maximum Independent Set (MIS), Quadratic Assignment Problem (QAP), and Market Share Problem (MSP). Our study evaluates gate-based quantum approaches, including the Variational Quantum Eigensolver (VQE) and its CVaR-enhanced variant, alongside advanced quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and its extensions. To address resource constraints, we incorporate qubit compression techniques like Pauli Correlation Encoding (PCE) and Quantum Random Access Optimization (QRAO). Experimental results, obtained from simulated quantum environments and classical solvers, provide key insights into feasibility, optimality gaps, and scalability. Our findings highlight both the promise and current limitations of quantum optimization, offering a structured pathway for future research and practical applications in quantum-enhanced decision-making.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

In recent years, quantum computing has emerged as a promising technology for solving complex computational problems. Generative modeling is a technique that allows us to learn and generate new data samples similar to the original dataset. In this paper, we propose a generative modeling approach using quantum gates to generate new samples from a given dataset. We start with a brief introduction to quantum computing and generative modeling. Then, we describe our proposed approach, which involves encoding the dataset into quantum states and using quantum gates to manipulate these states to generate new samples. We also provide mathematical details of our approach and demonstrate its effectiveness through experimental results on various datasets.

In image processing, the amount of data to be processed grows rapidly, in particular when imaging methods yield images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the Flexible Representation of Quantum Images (FRQI). Furthermore, we check experimentally what is the limit in the current noisy intermediate-scale quantum era, i.e. up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates needed, especially of the error-prone controlled-NOT gates, can be reduced. As a consequence, the size of manageable images increases.

This work endeavors to juxtapose the efficacy of machine learning algorithms within classical and quantum computational paradigms. Particularly, by emphasizing on Support Vector Machines (SVM), we scrutinize the classification prowess of classical SVM and Quantum Support Vector Machines (QSVM) operational on quantum hardware over the Iris dataset. The methodology embraced encapsulates an extensive array of experiments orchestrated through the Qiskit library, alongside hyperparameter optimization. The findings unveil that in particular scenarios, QSVMs extend a level of accuracy that can vie with classical SVMs, albeit the execution times are presently protracted. Moreover, we underscore that augmenting quantum computational capacity and the magnitude of parallelism can markedly ameliorate the performance of quantum machine learning algorithms. This inquiry furnishes invaluable insights regarding the extant scenario and future potentiality of machine learning applications in the quantum epoch. Colab: https://t.ly/QKuz0

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum-classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks but also highlights the substantial role of deep learning in advancing quantum machine learning.

Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli propagation has recently emerged as a promising new family of classical algorithms for simulating digital quantum systems. Here we provide a comprehensive account of Pauli propagation, tracing its algorithmic structure from its bit-level implementation and formulation as a tree-search problem, all the way to its high-level user applications for simulating quantum circuits and dynamics. Utilising these observations, we present PauliPropagation.jl, a Julia software package that can perform rapid Pauli propagation simulation straight out-of-the-box and can be used more generally as a building block for novel simulation algorithms.

Quantum Implicit Neural Representations (QINRs) include components for learning and execution on gate-based quantum computers. While QINRs recently emerged as a promising new paradigm, many challenges concerning their architecture and ansatz design, the utility of quantum-mechanical properties, training efficiency and the interplay with classical modules remain. This paper advances the field by introducing a new type of QINR for 2D image and 3D geometric field learning, which we collectively refer to as Quantum Visual Field (QVF). QVF encodes classical data into quantum statevectors using neural amplitude encoding grounded in a learnable energy manifold, ensuring meaningful Hilbert space embeddings. Our ansatz follows a fully entangled design of learnable parametrised quantum circuits, with quantum (unitary) operations performed in the real Hilbert space, resulting in numerically stable training with fast convergence. QVF does not rely on classical post-processing -- in contrast to the previous QINR learning approach -- and directly employs projective measurement to extract learned signals encoded in the ansatz. Experiments on a quantum hardware simulator demonstrate that QVF outperforms the existing quantum approach and widely used classical foundational baselines in terms of visual representation accuracy across various metrics and model characteristics, such as learning of high-frequency details. We also show applications of QVF in 2D and 3D field completion and 3D shape interpolation, highlighting its practical potential.

The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the MED is both more accurate and significantly more flexible.

Generative models are a class of machine learning models that aim to learn the underlying probability distribution of data. Unlike discriminative models, generative models focus on capturing the data's inherent structure, allowing them to generate new samples that resemble the original data. To fully exploit the potential of modeling probability distributions using quantum physics, a quantum-inspired generative model known as the Born machines have shown great advancements in learning classical and quantum data over matrix product state(MPS) framework. The Born machines support tractable log-likelihood, autoregressive and mask sampling, and have shown outstanding performance in various unsupervised learning tasks. However, much of the current research has been centered on improving the expressive power of MPS, predominantly embedding each token directly by a corresponding tensor index. In this study, we generalize the embedding method into trainable quantum measurement operators that can be simultaneously honed with MPS. Our study indicated that combined with trainable embedding, Born machines can exhibit better performance and learn deeper correlations from the dataset.

Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing quantum variational activation functions (QVAFs), realized through single-qubit data re-uploading circuits called DatA Re-Uploading ActivatioNs (DARUANs). We show that DARUAN with trainable weights in data pre-processing possesses an exponentially growing frequency spectrum with data repetitions, enabling an exponential reduction in parameter size compared with Fourier-based activations without loss of expressivity. Embedding DARUAN into KANs yields quantum-inspired KANs (QKANs), which retain the interpretability of KANs while improving their parameter efficiency, expressivity, and generalization. We further introduce two novel techniques to enhance scalability, feasibility and computational efficiency, such as layer extension and hybrid QKANs (HQKANs) as drop-in replacements of multi-layer perceptrons (MLPs) for feed-forward networks in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. DARUANs and QKANs offer a promising direction for advancing quantum machine learning on both noisy intermediate-scale quantum (NISQ) hardware and classical quantum simulators.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with 27 qubits on a superconducting processor.

The problem of minimizing the maximum of N convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring O(Nepsilon^{-2/3} + epsilon^{-8/3}) queries to a first-order oracle to compute an epsilon-suboptimal point. On the other hand, quantum algorithms for optimization are rapidly advancing with speedups shown on many important optimization problems. In this paper, we conduct a systematic study for quantum algorithms and lower bounds for minimizing the maximum of N convex, Lipschitz functions. On one hand, we develop quantum algorithms with an improved complexity bound of O(Nepsilon^{-5/3} + epsilon^{-8/3}). On the other hand, we prove that quantum algorithms must take Omega(Nepsilon^{-2/3}) queries to a first order quantum oracle, showing that our dependence on N is optimal up to poly-logarithmic factors.

In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.

The nexus of quantum computing and machine learning - quantum machine learning - offers the potential for significant advancements in chemistry. This review specifically explores the potential of quantum neural networks on gate-based quantum computers within the context of drug discovery. We discuss the theoretical foundations of quantum machine learning, including data encoding, variational quantum circuits, and hybrid quantum-classical approaches. Applications to drug discovery are highlighted, including molecular property prediction and molecular generation. We provide a balanced perspective, emphasizing both the potential benefits and the challenges that must be addressed.

The Monty Hall problem is a classic probability puzzle known for its counterintuitive solution, revealing fundamental discrepancies between mathematical reasoning and human intuition. To bridge this gap, we introduce a novel explanatory framework inspired by quantum measurement theory. Specifically, we conceptualize the hosts' actions-opening doors to reveal non-prizes-as analogous to quantum measurements that cause asymmetric collapses of the probability distribution. This quantum-inspired interpretation not only clarifies why the intuitive misunderstanding arises but also provides generalized formulas consistent with standard Bayesian results. We further validate our analytical approach using Monte Carlo simulations across various problem settings, demonstrating precise agreement between theoretical predictions and empirical outcomes. Our quantum analogy thus offers a powerful pedagogical tool, enhancing intuitive understanding of conditional probability phenomena through the lens of probability redistribution and quantum-like measurement operations.

We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS). Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians. This tailored approach has two clear advantages over previous algorithms that were designed to map a generic MPS to a quantum circuit. First, we optimize all parameters of a parametric circuit at once using Approximate Quantum Compiling (AQC) - this is to be contrasted with other approaches based on locally optimizing a subset of circuit parameters and "sweeping" across the system. We introduce an optimization scheme to avoid the so-called ``orthogonality catastrophe" - i.e. the fact that the fidelity of two arbitrary quantum states decays exponentially with the number of qubits - that would otherwise render a global optimization of the circuit impractical. Second, the depth of our parametric circuit is constant in the number of qubits for a fixed simulation time and fixed error tolerance. This is to be contrasted with the linear circuit Ansatz used in generic algorithms whose depth scales linearly in the number of qubits. For simulation problems on 100 qubits, we show that AQCtensor thus achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit, as compared with the best generic MPS to quantum circuit algorithms. We demonstrate our approach on simulation problems on Heisenberg-like Hamiltonians on up to 100 qubits and find optimized quantum circuits that have significantly reduced depth as compared to standard Trotterized circuits.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of simulating open quantum systems calls for the development of strategies to approximate their dynamics. In this paper, we present an approach for tackling open quantum system dynamics. Using an exact probabilistic formulation of quantum physics based on positive operator-valued measure (POVM), we compactly represent quantum states with autoregressive transformer neural networks; such networks bring significant algorithmic flexibility due to efficient exact sampling and tractable density. We further introduce the concept of String States to partially restore the symmetry of the autoregressive transformer neural network and improve the description of local correlations. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator using a forward-backward trapezoid method and find the steady state via a variational formulation. Our approach is benchmarked on prototypical one and two-dimensional systems, finding results which closely track the exact solution and achieve higher accuracy than alternative approaches based on using Markov chain Monte Carlo to sample restricted Boltzmann machines. Our work provides general methods for understanding quantum dynamics in various contexts, as well as techniques for solving high-dimensional probabilistic differential equations in classical setups.

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.

We introduce fusion-based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present strong evidence that commonly used models with provable absence of barren plateaus are also classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing quantum computers can be essential for collecting data, our analysis sheds serious doubt on the non-classicality of the information processing capabilities of parametrized quantum circuits for barren plateau-free landscapes. We end by discussing caveats in our arguments, the role of smart initializations and the possibility of provably superpolynomial, or simply practical, advantages from running parametrized quantum circuits.

The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle problem, the fixed-point quantum search with an optimal number of queries was proposed [Phys. Rev. Lett. 113, 210501 (2014)], which always finds a marked state with a high probability when a lower bound of the proportion of marked states is given. The fixed-point quantum search relies on a key lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials, but its proof is not given explicitly. In this work, we give a detailed proof of this lemma, thus providing a sound foundation for the correctness of the fixed-point quantum search. This lemma may be of independent interest as well, since it expands the mathematical form of the recursive relation of Chebyshev polynomials of the first kind, and it also constitutes a key component in overcoming the souffle problem of quantum walk-based search algorithms, for example, robust quantum walk search on complete bipartite graphs [Phys. Rev. A 106, 052207 (2022)]. Hopefully, more applications of the lemma will be found in the future.

Artificial neural networks are the heart of machine learning algorithms and artificial intelligence protocols. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt's `perceptron', but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a perceptron, which shows exponential advantage in encoding resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives remarkably good answers against the expected results. We show that this quantum model of a perceptron can be used as an elementary nonlinear classifier of simple patterns, as a first step towards practical training of artificial quantum neural networks to be efficiently implemented on near-term quantum processing hardware.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

Quantum architecture Search (QAS) is a promising direction for optimization and automated design of quantum circuits towards quantum advantage. Recent techniques in QAS emphasize Multi-Layer Perceptron (MLP)-based deep Q-networks. However, their interpretability remains challenging due to the large number of learnable parameters and the complexities involved in selecting appropriate activation functions. In this work, to overcome these challenges, we utilize the Kolmogorov-Arnold Network (KAN) in the QAS algorithm, analyzing their efficiency in the task of quantum state preparation and quantum chemistry. In quantum state preparation, our results show that in a noiseless scenario, the probability of success is 2 to 5 times higher than MLPs. In noisy environments, KAN outperforms MLPs in fidelity when approximating these states, showcasing its robustness against noise. In tackling quantum chemistry problems, we enhance the recently proposed QAS algorithm by integrating curriculum reinforcement learning with a KAN structure. This facilitates a more efficient design of parameterized quantum circuits by reducing the number of required 2-qubit gates and circuit depth. Further investigation reveals that KAN requires a significantly smaller number of learnable parameters compared to MLPs; however, the average time of executing each episode for KAN is higher.

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

We present an open-source database of superconducting quantum device designs that may be used as the starting point for customized devices. Each design can be generated programmatically using the open-source Qiskit Metal package, and simulated using finite-element electromagnetic solvers. We present a robust workflow for achieving high accuracy on design simulations. Many designs in the database are experimentally validated, showing excellent agreement between simulated and measured parameters. Our database includes a front-end interface that allows users to generate ``best-guess'' designs based on desired circuit parameters. This project lowers the barrier to entry for research groups seeking to make a new class of devices by providing them a well-characterized starting point from which to refine their designs.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

This paper introduces Quantum-PEFT that leverages quantum computations for parameter-efficient fine-tuning (PEFT). Unlike other additive PEFT methods, such as low-rank adaptation (LoRA), Quantum-PEFT exploits an underlying full-rank yet surprisingly parameter efficient quantum unitary parameterization. With the use of Pauli parameterization, the number of trainable parameters grows only logarithmically with the ambient dimension, as opposed to linearly as in LoRA-based PEFT methods. Quantum-PEFT achieves vanishingly smaller number of trainable parameters than the lowest-rank LoRA as dimensions grow, enhancing parameter efficiency while maintaining a competitive performance. We apply Quantum-PEFT to several transfer learning benchmarks in language and vision, demonstrating significant advantages in parameter efficiency.

Quantum algorithms for optimization problems are of general interest. Despite recent progress in classical lower bounds for nonconvex optimization under different settings and quantum lower bounds for convex optimization, quantum lower bounds for nonconvex optimization are still widely open. In this paper, we conduct a systematic study of quantum query lower bounds on finding epsilon-approximate stationary points of nonconvex functions, and we consider the following two important settings: 1) having access to p-th order derivatives; or 2) having access to stochastic gradients. The classical query lower bounds is Omegabig(epsilon^{-1+p{p}}big) regarding the first setting, and Omega(epsilon^{-4}) regarding the second setting (or Omega(epsilon^{-3}) if the stochastic gradient function is mean-squared smooth). In this paper, we extend all these classical lower bounds to the quantum setting. They match the classical algorithmic results respectively, demonstrating that there is no quantum speedup for finding epsilon-stationary points of nonconvex functions with p-th order derivative inputs or stochastic gradient inputs, whether with or without the mean-squared smoothness assumption. Technically, our quantum lower bounds are obtained by showing that the sequential nature of classical hard instances in all these settings also applies to quantum queries, preventing any quantum speedup other than revealing information of the stationary points sequentially.

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In this way, our protocol is compatible with various quantum machines and can be used to compile multi-qubit operators. We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets. In the task of single-qubit operator compiling, our proposal outperforms other RL-based quantum compilers in the measure of compiling sequence length and inference time. Meanwhile, the output solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably, for the inverse-free universal basis set, the achieved sequence length complexity is comparable with the inverse-based setting and dramatically advances previous methods. These empirical results contribute to improving the inverse-free Solovay-Kitaev theorem. In addition, for the first time, we demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit operator compiling. The achieved results open an avenue for integrating RL with quantum compiling to unify efficiency and practicality and thus facilitate the exploration of quantum advantages.

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements (mu, nu) are coupled to covariates, a challenging conditional distribution learning setting arises. Existing approaches for learning a global transport map parameterized through a potentially unseen context utilize Neural OT and largely rely on Brenier's theorem. Here, we propose a first-of-its-kind quantum computing formulation for amortized optimization of contextualized transportation plans. We exploit a direct link between doubly stochastic matrices and unitary operators thus unravelling a natural connection between OT and quantum computation. We verify our method (QontOT) on synthetic and real data by predicting variations in cell type distributions conditioned on drug dosage. Importantly we conduct a 24-qubit hardware experiment on a task challenging for classical computers and report a performance that cannot be matched with our classical neural OT approach. In sum, this is a first step toward learning to predict contextualized transportation plans through quantum computing.

Code Large Language Models (Code LLMs) have emerged as powerful tools, revolutionizing the software development landscape by automating the coding process and reducing time and effort required to build applications. This paper focuses on training Code LLMs to specialize in the field of quantum computing. We begin by discussing the unique needs of quantum computing programming, which differ significantly from classical programming approaches or languages. A Code LLM specializing in quantum computing requires a foundational understanding of quantum computing and quantum information theory. However, the scarcity of available quantum code examples and the rapidly evolving field, which necessitates continuous dataset updates, present significant challenges. Moreover, we discuss our work on training Code LLMs to produce high-quality quantum code using the Qiskit library. This work includes an examination of the various aspects of the LLMs used for training and the specific training conditions, as well as the results obtained with our current models. To evaluate our models, we have developed a custom benchmark, similar to HumanEval, which includes a set of tests specifically designed for the field of quantum computing programming using Qiskit. Our findings indicate that our model outperforms existing state-of-the-art models in quantum computing tasks. We also provide examples of code suggestions, comparing our model to other relevant code LLMs. Finally, we introduce a discussion on the potential benefits of Code LLMs for quantum computing computational scientists, researchers, and practitioners. We also explore various features and future work that could be relevant in this context.

Large language models (LLM) have achieved remarkable outcomes in addressing complex problems, including math, coding, and analyzing large amounts of scientific reports. Yet few works have explored the potential of LLM in quantum computing. The most challenging problem is how to leverage LLMs to automatically generate quantum circuits at a large scale. In this paper, we address such a challenge by fine-tuning LLMs and injecting the domain-specific knowledge of quantum computing. In particular, we investigate the mechanisms to generate training data sets and construct the end-to-end pipeline to fine-tune pre-trained LLMs that produce parameterized quantum circuits for optimization problems. We have prepared 14,000 quantum circuits covering a substantial part of the quantum optimization landscape: 12 optimization problem instances and their optimized QAOA, VQE, and adaptive VQE circuits. The fine-tuned LLMs can construct syntactically correct parametrized quantum circuits in the most recent OpenQASM 3.0. We have evaluated the quality of the parameters by comparing them to the optimized expectation values and distributions. Our evaluation shows that the fine-tuned LLM outperforms state-of-the-art models and that the parameters are better than random. The LLM-generated parametrized circuits and initial parameters can be used as a starting point for further optimization, e.g., templates in quantum machine learning and the benchmark for compilers and hardware.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

The emerging field of quantum computing has shown it might change how we process information by using the unique principles of quantum mechanics. As researchers continue to push the boundaries of quantum technologies to unprecedented levels, distributed quantum computing raises as an obvious path to explore with the aim of boosting the computational power of current quantum systems. This paper presents a comprehensive survey of the current state of the art in the distributed quantum computing field, exploring its foundational principles, landscape of achievements, challenges, and promising directions for further research. From quantum communication protocols to entanglement-based distributed algorithms, each aspect contributes to the mosaic of distributed quantum computing, making it an attractive approach to address the limitations of classical computing. Our objective is to provide an exhaustive overview for experienced researchers and field newcomers.

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulators and hardware. Our framework is applied to three representative NP-hard problems: the Travelling Salesman Problem (TSP), the Multi-Dimensional Knapsack Problem (MDKP), and the Maximum Independent Set (MIS). We demonstrate that MDKP and TSP, with their inequality-based or degree-constrained structures, allow for slack-free reformulations, leading to significant qubit savings without compromising performance. In contrast, MIS does not inherently benefit from slack elimination but still gains in feasibility and objective quality from principled Lagrangian updates. We benchmark these methods across classically hard instances, analyzing trade-offs in qubit usage, feasibility, and optimality gaps. Our results highlight the flexibility of Lagrangian formulations as a scalable alternative to naive QUBO penalization, even when qubit savings are not always achievable. This work provides practical insights for deploying constraint-aware quantum optimization pipelines, with applications in logistics, network design, and resource allocation.

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

In this research, we explore the integration of quantum computing with classical machine learning for image classification tasks, specifically focusing on the MNIST dataset. We propose a hybrid quantum-classical approach that leverages the strengths of both paradigms. The process begins with preprocessing the MNIST dataset, normalizing the pixel values, and reshaping the images into vectors. An autoencoder compresses these 784-dimensional vectors into a 64-dimensional latent space, effectively reducing the data's dimensionality while preserving essential features. These compressed features are then processed using a quantum circuit implemented on a 5-qubit system. The quantum circuit applies rotation gates based on the feature values, followed by Hadamard and CNOT gates to entangle the qubits, and measurements are taken to generate quantum outcomes. These outcomes serve as input for a classical neural network designed to classify the MNIST digits. The classical neural network comprises multiple dense layers with batch normalization and dropout to enhance generalization and performance. We evaluate the performance of this hybrid model and compare it with a purely classical approach. The experimental results indicate that while the hybrid model demonstrates the feasibility of integrating quantum computing with classical techniques, the accuracy of the final model, trained on quantum outcomes, is currently lower than the classical model trained on compressed features. This research highlights the potential of quantum computing in machine learning, though further optimization and advanced quantum algorithms are necessary to achieve superior performance.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

This article aims to investigate how circuit-based hybrid Quantum Convolutional Neural Networks (QCNNs) can be successfully employed as image classifiers in the context of remote sensing. The hybrid QCNNs enrich the classical architecture of CNNs by introducing a quantum layer within a standard neural network. The novel QCNN proposed in this work is applied to the Land Use and Land Cover (LULC) classification, chosen as an Earth Observation (EO) use case, and tested on the EuroSAT dataset used as reference benchmark. The results of the multiclass classification prove the effectiveness of the presented approach, by demonstrating that the QCNN performances are higher than the classical counterparts. Moreover, investigation of various quantum circuits shows that the ones exploiting quantum entanglement achieve the best classification scores. This study underlines the potentialities of applying quantum computing to an EO case study and provides the theoretical and experimental background for futures investigations.

Many hybrid quantum-classical algorithms for the application of ground state energy estimation in quantum chemistry involve estimating the expectation value of a molecular Hamiltonian with respect to a quantum state through measurements on a quantum device. To guide the selection of measurement methods designed for this observable estimation problem, we propose a benchmark called CSHOREBench (Common States and Hamiltonians for ObseRvable Estimation Benchmark) that assesses the performance of these methods against a set of common molecular Hamiltonians and common states encountered during the runtime of hybrid quantum-classical algorithms. In CSHOREBench, we account for resource utilization of a quantum computer through measurements of a prepared state, and a classical computer through computational runtime spent in proposing measurements and classical post-processing of acquired measurement outcomes. We apply CSHOREBench considering a variety of measurement methods on Hamiltonians of size up to 16 qubits. Our discussion is aided by using the framework of decision diagrams which provides an efficient data structure for various randomized methods and illustrate how to derandomize distributions on decision diagrams. In numerical simulations, we find that the methods of decision diagrams and derandomization are the most preferable. In experiments on IBM quantum devices against small molecules, we observe that decision diagrams reduces the number of measurements made by classical shadows by more than 80%, that made by locally biased classical shadows by around 57%, and consistently require fewer quantum measurements along with lower classical computational runtime than derandomization. Furthermore, CSHOREBench is empirically efficient to run when considering states of random quantum ansatz with fixed depth.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models. Our experiments reveal that state-of-the-art quantum neural networks accurately fit random states and random labeling of training data. This ability to memorize random data defies current notions of small generalization error, problematizing approaches that build on complexity measures such as the VC dimension, the Rademacher complexity, and all their uniform relatives. We complement our empirical results with a theoretical construction showing that quantum neural networks can fit arbitrary labels to quantum states, hinting at their memorization ability. Our results do not preclude the possibility of good generalization with few training data but rather rule out any possible guarantees based only on the properties of the model family. These findings expose a fundamental challenge in the conventional understanding of generalization in quantum machine learning and highlight the need for a paradigm shift in the design of quantum models for machine learning tasks.

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.

We implement physics-informed neural networks (PINNs) to solve the time-independent Schr\"odinger equation for three canonical one-dimensional quantum potentials: an infinite square well, a finite square well, and a finite barrier. The PINN models incorporate trial wavefunctions that exactly satisfy boundary conditions (Dirichlet zeros at domain boundaries), and they optimize a loss functional combining the PDE residual with a normalization constraint. For the infinite well, the ground-state energy is known (E = pi^2 in dimensionless units) and held fixed in training, whereas for the finite well and barrier, the eigenenergy is treated as a trainable parameter. We use fully-connected neural networks with smooth activation functions to represent the wavefunction and demonstrate that PINNs can learn the ground-state eigenfunctions and eigenvalues for these quantum systems. The results show that the PINN-predicted wavefunctions closely match analytical solutions or expected behaviors, and the learned eigenenergies converge to known values. We present training logs and convergence of the energy parameter, as well as figures comparing the PINN solutions to exact results. The discussion addresses the performance of PINNs relative to traditional numerical methods, highlighting challenges such as convergence to the correct eigenvalue, sensitivity to initialization, and the difficulty of modeling discontinuous potentials. We also discuss the importance of the normalization term to resolve the scaling ambiguity of the wavefunction. Finally, we conclude that PINNs are a viable approach for quantum eigenvalue problems, and we outline future directions including extensions to higher-dimensional and time-dependent Schr\"odinger equations.

Ridgelet transform has been a fundamental mathematical tool in the theoretical studies of neural networks. However, the practical applicability of ridgelet transform to conducting learning tasks was limited since its numerical implementation by conventional classical computation requires an exponential runtime exp(O(D)) as data dimension D increases. To address this problem, we develop a quantum ridgelet transform (QRT), which implements the ridgelet transform of a quantum state within a linear runtime O(D) of quantum computation. As an application, we also show that one can use QRT as a fundamental subroutine for quantum machine learning (QML) to efficiently find a sparse trainable subnetwork of large shallow wide neural networks without conducting large-scale optimization of the original network. This application discovers an efficient way in this regime to demonstrate the lottery ticket hypothesis on finding such a sparse trainable neural network. These results open an avenue of QML for accelerating learning tasks with commonly used classical neural networks.

Pruning neural networks, which involves removing a fraction of their weights, can often maintain high accuracy while significantly reducing model complexity, at least up to a certain limit. We present a neural network pruning technique that builds upon the Combinatorial Brain Surgeon, but solves an optimization problem over a subset of the network weights in an iterative, block-wise manner using block coordinate descent. The iterative, block-based nature of this pruning technique, which we dub ``iterative Combinatorial Brain Surgeon'' (iCBS) allows for scalability to very large models, including large language models (LLMs), that may not be feasible with a one-shot combinatorial optimization approach. When applied to large models like Mistral and DeiT, iCBS achieves higher performance metrics at the same density levels compared to existing pruning methods such as Wanda. This demonstrates the effectiveness of this iterative, block-wise pruning method in compressing and optimizing the performance of large deep learning models, even while optimizing over only a small fraction of the weights. Moreover, our approach allows for a quality-time (or cost) tradeoff that is not available when using a one-shot pruning technique alone. The block-wise formulation of the optimization problem enables the use of hardware accelerators, potentially offsetting the increased computational costs compared to one-shot pruning methods like Wanda. In particular, the optimization problem solved for each block is quantum-amenable in that it could, in principle, be solved by a quantum computer.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

In recent years, Classical Convolutional Neural Networks (CNNs) have been applied for image recognition successfully. Quantum Convolutional Neural Networks (QCNNs) are proposed as a novel generalization to CNNs by using quantum mechanisms. The quantum mechanisms lead to an efficient training process in QCNNs by reducing the size of input from N to log_2N. This paper implements and compares both CNNs and QCNNs by testing losses and prediction accuracy on three commonly used datasets. The datasets include the MNIST hand-written digits, Fashion MNIST and cat/dog face images. Additionally, data augmentation (DA), a technique commonly used in CNNs to improve the performance of classification by generating similar images based on original inputs, is also implemented in QCNNs. Surprisingly, the results showed that data augmentation didn't improve QCNNs performance. The reasons and logic behind this result are discussed, hoping to expand our understanding of Quantum machine learning theory.

Simulation-based optimization is a widely used method to solve stochastic optimization problems. This method aims to identify an optimal solution by maximizing the expected value of the objective function. However, due to its computational complexity, the function cannot be accurately evaluated directly, hence it is estimated through simulation. Exploiting the enhanced efficiency of Quantum Amplitude Estimation (QAE) compared to classical Monte Carlo simulation, it frequently outpaces classical simulation-based optimization, resulting in notable performance enhancements in various scenarios. In this work, we make use of a quantum-enhanced algorithm for simulation-based optimization and apply it to solve a variant of the classical Newsvendor problem which is known to be NP-hard. Such problems provide the building block for supply chain management, particularly in inventory management and procurement optimization under risks and uncertainty

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

The key challenge in the noisy intermediate-scale quantum era is finding useful circuits compatible with current device limitations. Variational quantum algorithms (VQAs) offer a potential solution by fixing the circuit architecture and optimizing individual gate parameters in an external loop. However, parameter optimization can become intractable, and the overall performance of the algorithm depends heavily on the initially chosen circuit architecture. Several quantum architecture search (QAS) algorithms have been developed to design useful circuit architectures automatically. In the case of parameter optimization alone, noise effects have been observed to dramatically influence the performance of the optimizer and final outcomes, which is a key line of study. However, the effects of noise on the architecture search, which could be just as critical, are poorly understood. This work addresses this gap by introducing a curriculum-based reinforcement learning QAS (CRLQAS) algorithm designed to tackle challenges in realistic VQA deployment. The algorithm incorporates (i) a 3D architecture encoding and restrictions on environment dynamics to explore the search space of possible circuits efficiently, (ii) an episode halting scheme to steer the agent to find shorter circuits, and (iii) a novel variant of simultaneous perturbation stochastic approximation as an optimizer for faster convergence. To facilitate studies, we developed an optimized simulator for our algorithm, significantly improving computational efficiency in simulating noisy quantum circuits by employing the Pauli-transfer matrix formalism in the Pauli-Liouville basis. Numerical experiments focusing on quantum chemistry tasks demonstrate that CRLQAS outperforms existing QAS algorithms across several metrics in both noiseless and noisy environments.

Deep Reinforcement Learning is emerging as a promising approach for the continuous control task of robotic arm movement. However, the challenges of learning robust and versatile control capabilities are still far from being resolved for real-world applications, mainly because of two common issues of this learning paradigm: the exploration strategy and the slow learning speed, sometimes known as "the curse of dimensionality". This work aims at exploring and assessing the advantages of the application of Quantum Computing to one of the state-of-art Reinforcement Learning techniques for continuous control - namely Soft Actor-Critic. Specifically, the performance of a Variational Quantum Soft Actor-Critic on the movement of a virtual robotic arm has been investigated by means of digital simulations of quantum circuits. A quantum advantage over the classical algorithm has been found in terms of a significant decrease in the amount of required parameters for satisfactory model training, paving the way for further promising developments.

The Sachdev-Ye-Kitaev (SYK) model, known for its strong quantum correlations and chaotic behavior, serves as a key platform for quantum gravity studies. However, variationally preparing thermal states on near-term quantum processors for large systems (N>12, where N is the number of Majorana fermions) presents a significant challenge due to the rapid growth in the complexity of parameterized quantum circuits. This paper addresses this challenge by integrating reinforcement learning (RL) with convolutional neural networks, employing an iterative approach to optimize the quantum circuit and its parameters. The refinement process is guided by a composite reward signal derived from entropy and the expectation values of the SYK Hamiltonian. This approach reduces the number of CNOT gates by two orders of magnitude for systems Ngeq12 compared to traditional methods like first-order Trotterization. We demonstrate the effectiveness of the RL framework in both noiseless and noisy quantum hardware environments, maintaining high accuracy in thermal state preparation. This work advances a scalable, RL-based framework with applications for quantum gravity studies and out-of-time-ordered thermal correlators computation in quantum many-body systems on near-term quantum hardware. The code is available at https://github.com/Aqasch/solving_SYK_model_with_RL.

Quantum computing promises to enhance machine learning and artificial intelligence. Different quantum algorithms have been proposed to improve a wide spectrum of machine learning tasks. Yet, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from the vulnerability problem: adding tiny carefully-crafted perturbations to the legitimate original data samples would facilitate incorrect predictions at a notably high confidence level. This will pose serious problems for future quantum machine learning applications in safety and security-critical scenarios. Here, we report the first experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built upon variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 mus, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4% respectively, with both real-life images (e.g., medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would significantly enhance their robustness to such perturbations. Our results reveal experimentally a crucial vulnerability aspect of quantum learning systems under adversarial scenarios and demonstrate an effective defense strategy against adversarial attacks, which provide a valuable guide for quantum artificial intelligence applications with both near-term and future quantum devices.

The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

In recent years, there has been an emerging trend of combining two innovations in computer science and physics to achieve better computation capability. Exploring the potential of quantum computation to achieve highly efficient performance in various tasks is a vital development in engineering and a valuable question in sciences, as it has a significant potential to provide exponential speedups for technologically complex problems that are specifically advantageous to quantum computers. However, one key issue in unleashing this potential is constructing an efficient approach to load classical data into quantum states that can be executed by quantum computers or quantum simulators on classical hardware. Therefore, the split-step quantum walks (SSQW) algorithm was proposed to address this limitation. We facilitate SSQW to design parameterized quantum circuits (PQC) that can generate probability distributions and optimize the parameters to achieve the desired distribution using a variational solver. A practical example of implementing SSQW using Qiskit has been released as open-source software. Showing its potential as a promising method for generating desired probability amplitude distributions highlights the potential application of SSQW in option pricing through quantum simulation.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

This article introduces an innovative interactive visualization tool designed to demystify quantum machine learning (QML) algorithms. Our work is inspired by the success of classical machine learning visualization tools, such as TensorFlow Playground, and aims to bridge the gap in visualization resources specifically for the field of QML. The article includes a comprehensive overview of relevant visualization metaphors from both quantum computing and classical machine learning, the development of an algorithm visualization concept, and the design of a concrete implementation as an interactive web application. By combining common visualization metaphors for the so-called data re-uploading universal quantum classifier as a representative QML model, this article aims to lower the entry barrier to quantum computing and encourage further innovation in the field. The accompanying interactive application is a proposal for the first version of a quantum machine learning playground for learning and exploring QML models.

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.

Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H_2, HeH^+, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H_2 from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits.

Energy filter methods in combination with quantum simulation can efficiently access the properties of quantum many-body systems at finite energy densities [Lu et al. PRX Quantum 2, 020321 (2021)]. Classically simulating this algorithm with tensor networks can be used to investigate the microcanonical properties of large spin chains, as recently shown in [Yang et al. Phys. Rev. B 106, 024307 (2022)]. Here we extend this strategy to explore the properties of off-diagonal matrix elements of observables in the energy eigenbasis, fundamentally connected to the thermalization behavior and the eigenstate thermalization hypothesis. We test the method on integrable and non-integrable spin chains of up to 60 sites, much larger than accessible with exact diagonalization. Our results allow us to explore the scaling of the off-diagonal functions with the size and energy difference, and to establish quantitative differences between integrable and non-integrable cases.

The emergence of hybrid quantum-classical machine learning (HQML) models opens new horizons of computational intelligence but their fundamental complexity frequently leads to black box behavior that undermines transparency and reliability in their application. Although XAI for quantum systems still in its infancy, a major research gap is evident in robust global and local explainability approaches that are designed for HQML architectures that employ quantized feature encoding followed by classical learning. The gap is the focus of this work, which introduces QuXAI, an framework based upon Q-MEDLEY, an explainer for explaining feature importance in these hybrid systems. Our model entails the creation of HQML models incorporating quantum feature maps, the use of Q-MEDLEY, which combines feature based inferences, preserving the quantum transformation stage and visualizing the resulting attributions. Our result shows that Q-MEDLEY delineates influential classical aspects in HQML models, as well as separates their noise, and competes well against established XAI techniques in classical validation settings. Ablation studies more significantly expose the virtues of the composite structure used in Q-MEDLEY. The implications of this work are critically important, as it provides a route to improve the interpretability and reliability of HQML models, thus promoting greater confidence and being able to engage in safer and more responsible use of quantum-enhanced AI technology.

Quantum Machine Learning (QML) has surfaced as a pioneering framework addressing sequential control tasks and time-series modeling. It has demonstrated empirical quantum advantages notably within domains such as Reinforcement Learning (RL) and time-series prediction. A significant advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically tailored for memory-intensive tasks encompassing partially observable environments and non-linear time-series prediction. Nevertheless, QRNN-based models encounter challenges, notably prolonged training duration stemming from the necessity to compute quantum gradients using backpropagation-through-time (BPTT). This predicament exacerbates when executing the complete model on quantum devices, primarily due to the substantial demand for circuit evaluation arising from the parameter-shift rule. This paper introduces the Quantum Fast Weight Programmers (QFWP) as a solution to the temporal or sequential learning challenge. The QFWP leverages a classical neural network (referred to as the 'slow programmer') functioning as a quantum programmer to swiftly modify the parameters of a variational quantum circuit (termed the 'fast programmer'). Instead of completely overwriting the fast programmer at each time-step, the slow programmer generates parameter changes or updates for the quantum circuit parameters. This approach enables the fast programmer to incorporate past observations or information. Notably, the proposed QFWP model achieves learning of temporal dependencies without necessitating the use of quantum recurrent neural networks. Numerical simulations conducted in this study showcase the efficacy of the proposed QFWP model in both time-series prediction and RL tasks. The model exhibits performance levels either comparable to or surpassing those achieved by QLSTM-based models.

In this work, we address the problem of automating quantum variational machine learning. We develop a multi-locality parallelizable search algorithm, called MUSE, to find the initial points and the sets of parameters that achieve the best performance for quantum variational circuit learning. Simulations with five real-world classification datasets indicate that on average, MUSE improves the detection accuracy of quantum variational classifiers 2.3 times with respect to the observed lowest scores. Moreover, when applied to two real-world regression datasets, MUSE improves the quality of the predictions from negative coefficients of determination to positive ones. Furthermore, the classification and regression scores of the quantum variational models trained with MUSE are on par with the classical counterparts.

The distribution of high-quality Greenberger-Horne-Zeilinger (GHZ) states is at the heart of many quantum communication tasks, ranging from extending the baseline of telescopes to secret sharing. They also play an important role in error-correction architectures for distributed quantum computation, where Bell pairs can be leveraged to create an entangled network of quantum computers. We investigate the creation and distillation of GHZ states out of non-perfect Bell pairs over quantum networks. In particular, we introduce a heuristic dynamic programming algorithm to optimize over a large class of protocols that create and purify GHZ states. All protocols considered use a common framework based on measurements of non-local stabilizer operators of the target state (i.e., the GHZ state), where each non-local measurement consumes another (non-perfect) entangled state as a resource. The new protocols outperform previous proposals for scenarios without decoherence and local gate noise. Furthermore, the algorithms can be applied for finding protocols for any number of parties and any number of entangled pairs involved.

Breakthroughs in machine learning (ML) and advances in quantum computing (QC) drive the interdisciplinary field of quantum machine learning to new levels. However, due to the susceptibility of ML models to adversarial attacks, practical use raises safety-critical concerns. Existing Randomized Smoothing (RS) certification methods for classical machine learning models are computationally intensive. In this paper, we propose the combination of QC and the concept of discrete randomized smoothing to speed up the stochastic certification of ML models for discrete data. We show how to encode all the perturbations of the input binary data in superposition and use Quantum Amplitude Estimation (QAE) to obtain a quadratic reduction in the number of calls to the model that are required compared to traditional randomized smoothing techniques. In addition, we propose a new binary threat model to allow for an extensive evaluation of our approach on images, graphs, and text.

In this research, a comparative study of four Quantum Machine Learning (QML) models was conducted for fraud detection in finance. We proved that the Quantum Support Vector Classifier model achieved the highest performance, with F1 scores of 0.98 for fraud and non-fraud classes. Other models like the Variational Quantum Classifier, Estimator Quantum Neural Network (QNN), and Sampler QNN demonstrate promising results, propelling the potential of QML classification for financial applications. While they exhibit certain limitations, the insights attained pave the way for future enhancements and optimisation strategies. However, challenges exist, including the need for more efficient Quantum algorithms and larger and more complex datasets. The article provides solutions to overcome current limitations and contributes new insights to the field of Quantum Machine Learning in fraud detection, with important implications for its future development.

This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achieving a perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterized gate selection, and the integration of the quantum layer with classical neural network components. This work contributes to the growing body of research on hybrid quantum-classical models and their applicability to real-world datasets.

In the emergent realm of quantum computing, the Variational Quantum Eigensolver (VQE) stands out as a promising algorithm for solving complex quantum problems, especially in the noisy intermediate-scale quantum (NISQ) era. However, the ubiquitous presence of noise in quantum devices often limits the accuracy and reliability of VQE outcomes. This research introduces a novel approach to ameliorate this challenge by utilizing neural networks for zero noise extrapolation (ZNE) in VQE computations. By employing the Qiskit framework, we crafted parameterized quantum circuits using the RY-RZ ansatz and examined their behavior under varying levels of depolarizing noise. Our investigations spanned from determining the expectation values of a Hamiltonian, defined as a tensor product of Z operators, under different noise intensities to extracting the ground state energy. To bridge the observed outcomes under noise with the ideal noise-free scenario, we trained a Feed Forward Neural Network on the error probabilities and their associated expectation values. Remarkably, our model proficiently predicted the VQE outcome under hypothetical noise-free conditions. By juxtaposing the simulation results with real quantum device executions, we unveiled the discrepancies induced by noise and showcased the efficacy of our neural network-based ZNE technique in rectifying them. This integrative approach not only paves the way for enhanced accuracy in VQE computations on NISQ devices but also underlines the immense potential of hybrid quantum-classical paradigms in circumventing the challenges posed by quantum noise. Through this research, we envision a future where quantum algorithms can be reliably executed on noisy devices, bringing us one step closer to realizing the full potential of quantum computing.

Quantum machine learning implemented by variational quantum circuits (VQCs) is considered a promising concept for the noisy intermediate-scale quantum computing era. Focusing on applications in quantum reinforcement learning, we propose a specific action decoding procedure for a quantum policy gradient approach. We introduce a novel quality measure that enables us to optimize the classical post-processing required for action selection, inspired by local and global quantum measurements. The resulting algorithm demonstrates a significant performance improvement in several benchmark environments. With this technique, we successfully execute a full training routine on a 5-qubit hardware device. Our method introduces only negligible classical overhead and has the potential to improve VQC-based algorithms beyond the field of quantum reinforcement learning.

Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It helps preserve image quality and interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This study introduces a quantum convolutional autoencoder (QCAE) method for improved image denoising. This method was developed by substituting the representative latent space of the autoencoder with a quantum circuit. To enhance efficiency, we leveraged the advantages of the quantum approximate optimization algorithm (QAOA)-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

In recent years, there has been tremendous progress in the development of quantum computing hardware, algorithms and services leading to the expectation that in the near future quantum computers will be capable of performing simulations for natural science applications, operations research, and machine learning at scales mostly inaccessible to classical computers. Whereas the impact of quantum computing has already started to be recognized in fields such as cryptanalysis, natural science simulations, and optimization among others, very little is known about the full potential of quantum computing simulations and machine learning in the realm of healthcare and life science (HCLS). Herein, we discuss the transformational changes we expect from the use of quantum computation for HCLS research, more specifically in the field of cell-centric therapeutics. Moreover, we identify and elaborate open problems in cell engineering, tissue modeling, perturbation modeling, and bio-topology while discussing candidate quantum algorithms for research on these topics and their potential advantages over classical computational approaches.

In this work, we describe strategies and provide case-study activities that can be used to examine the properties of superposition, entanglement, tagging, complementarity, and measurement in quantum curricula geared for teacher training. Having a solid foundation in these conceptual ideas is critical for educators who will be adopting quantum ideas within the classroom. Yet they are some of the most difficult concepts to master. We show how one can systematically develop these conceptual foundations with thought experiments on light and with thought experiments that employ the Stern-Gerlach experiment. We emphasize the importance of computer animations in aiding the instruction on these concepts.

Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations and hype surrounding quantum computing we ask the question which are the promising applications to realize quantum advantage. We argue that small data problems and quantum algorithms with super-quadratic speedups are essential to make quantum computers useful in practice. With these guidelines one can separate promising applications for quantum computing from those where classical solutions should be pursued. While most of the proposed quantum algorithms and applications do not achieve the necessary speedups to be considered practical, we already see a huge potential in material science and chemistry. We expect further applications to be developed based on our guidelines.

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the kappa=pm1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10^{-8} Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schr\"odinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

Supervised machine learning approaches have been increasingly used in accelerating electronic structure prediction as surrogates of first-principle computational methods, such as density functional theory (DFT). While numerous quantum chemistry datasets focus on chemical properties and atomic forces, the ability to achieve accurate and efficient prediction of the Hamiltonian matrix is highly desired, as it is the most important and fundamental physical quantity that determines the quantum states of physical systems and chemical properties. In this work, we generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories and 130,831 stable molecular geometries, based on the QM9 dataset. By designing benchmark tasks with various molecules, we show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules. Both the QH9 dataset and the baseline models are provided to the community through an open-source benchmark, which can be highly valuable for developing machine learning methods and accelerating molecular and materials design for scientific and technological applications. Our benchmark is publicly available at https://github.com/divelab/AIRS/tree/main/OpenDFT/QHBench.

Quantum algorithms, represented as quantum circuits, can be used as benchmarks for assessing the performance of quantum systems. Existing datasets, widely utilized in the field, suffer from limitations in size and versatility, leading researchers to employ randomly generated circuits. Random circuits are, however, not representative benchmarks as they lack the inherent properties of real quantum algorithms for which the quantum systems are manufactured. This shortage of `useful' quantum benchmarks poses a challenge to advancing the development and comparison of quantum compilers and hardware. This research aims to enhance the existing quantum circuit datasets by generating what we refer to as `realistic-looking' circuits by employing the Transformer machine learning architecture. For this purpose, we introduce KetGPT, a tool that generates synthetic circuits in OpenQASM language, whose structure is based on quantum circuits derived from existing quantum algorithms and follows the typical patterns of human-written algorithm-based code (e.g., order of gates and qubits). Our three-fold verification process, involving manual inspection and Qiskit framework execution, transformer-based classification, and structural analysis, demonstrates the efficacy of KetGPT in producing large amounts of additional circuits that closely align with algorithm-based structures. Beyond benchmarking, we envision KetGPT contributing substantially to AI-driven quantum compilers and systems.

Topological data analysis (TDA) is a powerful technique for extracting complex and valuable shape-related summaries of high-dimensional data. However, the computational demands of classical algorithms for computing TDA are exorbitant, and quickly become impractical for high-order characteristics. Quantum computers offer the potential of achieving significant speedup for certain computational problems. Indeed, TDA has been purported to be one such problem, yet, quantum computing algorithms proposed for the problem, such as the original Quantum TDA (QTDA) formulation by Lloyd, Garnerone and Zanardi, require fault-tolerance qualifications that are currently unavailable. In this study, we present NISQ-TDA, a fully implemented end-to-end quantum machine learning algorithm needing only a short circuit-depth, that is applicable to high-dimensional classical data, and with provable asymptotic speedup for certain classes of problems. The algorithm neither suffers from the data-loading problem nor does it need to store the input data on the quantum computer explicitly. The algorithm was successfully executed on quantum computing devices, as well as on noisy quantum simulators, applied to small datasets. Preliminary empirical results suggest that the algorithm is robust to noise.

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

Generating entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote entanglement generation have been proposed, of which many have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D J_1-J_2 Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for scientific simulations of quantum many-body physics and quantum technology.

In this paper, we have studied the performance and role of local optimizers in quantum variational circuits. We studied the performance of the two most popular optimizers and compared their results with some popular classical machine learning algorithms. The classical algorithms we used in our study are support vector machine (SVM), gradient boosting (GB), and random forest (RF). These were compared with a variational quantum classifier (VQC) using two sets of local optimizers viz AQGD and COBYLA. For experimenting with VQC, IBM Quantum Experience and IBM Qiskit was used while for classical machine learning models, sci-kit learn was used. The results show that machine learning on noisy immediate scale quantum machines can produce comparable results as on classical machines. For our experiments, we have used a popular restaurant sentiment analysis dataset. The extracted features from this dataset and then after applying PCA reduced the feature set into 5 features. Quantum ML models were trained using 100 epochs and 150 epochs on using EfficientSU2 variational circuit. Overall, four Quantum ML models were trained and three Classical ML models were trained. The performance of the trained models was evaluated using standard evaluation measures viz, Accuracy, Precision, Recall, F-Score. In all the cases AQGD optimizer-based model with 100 Epochs performed better than all other models. It produced an accuracy of 77% and an F-Score of 0.785 which were highest across all the trained models.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

Qiskit is an open-source quantum computing framework that allows users to design, simulate, and run quantum circuits on real quantum hardware. We explore post-training techniques for LLMs to assist in writing Qiskit code. We introduce quantum verification as an effective method for ensuring code quality and executability on quantum hardware. To support this, we developed a synthetic data pipeline that generates quantum problem-unit test pairs and used it to create preference data for aligning LLMs with DPO. Additionally, we trained models using GRPO, leveraging quantum-verifiable rewards provided by the quantum hardware. Our best-performing model, combining DPO and GRPO, surpasses the strongest open-source baselines on the challenging Qiskit-HumanEval-hard benchmark.