Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resource Estimation for Quantum Variational Simulations of the Hubbard
  Model   As the advances in quantum hardware bring us into the noisy
intermediate-scale quantum (NISQ) era, one possible task we can perform without
quantum error correction using NISQ machines is the variational quantum
eigensolver (VQE) due to its shallow depth. A specific problem that we can
tackle is the strongly interacting Fermi-Hubbard model, which is classically
intractable and has practical implications in areas like superconductivity. In
this Article, we outline the details about the gate sequence, the measurement
scheme and the relevant error mitigation techniques for the implementation of
the Hubbard VQE on a NISQ platform. We perform resource estimation for both
silicon spin qubits and superconducting qubits for a 50-qubit simulation, which
cannot be solved exactly via classical means, and find similar results. The
number of two-qubit gates required is on the order of 20000. Hence, to suppress
the mean circuit error count to a level such that we can obtain meaningful
results with the aid of error mitigation, we need to achieve a two-qubit gate
error rate of $\sim 10^{-4}$. When searching for the ground state, we need a
few days for one gradient-descent iteration, which is impractical. This can be
reduced to around $10$ minutes if we distribute our task among hundreds of
quantum processing units. Hence, implementing a 50-qubit Hubbard model VQE on a
NISQ machine can be on the brink of being feasible in near term, but further
optimisation of our simulation scheme, improvements in the gate fidelity,
improvements in the optimisation scheme and advances in the error mitigation
techniques are needed to overcome the remaining obstacles. The scalability of
the hardware platform is also essential to overcome the runtime issue via
parallelisation, which can be done on one single silicon multi-core processor
or across multiple superconducting processors.

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th