Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling-based sublinear low-rank matrix arithmetic framework for
  dequantizing quantum machine learning   We present an algorithmic framework for quantum-inspired classical algorithms
on close-to-low-rank matrices, generalizing the series of results started by
Tang's breakthrough quantum-inspired algorithm for recommendation systems
[STOC'19]. Motivated by quantum linear algebra algorithms and the quantum
singular value transformation (SVT) framework of Gily\'en et al. [STOC'19], we
develop classical algorithms for SVT that run in time independent of input
dimension, under suitable quantum-inspired sampling assumptions. Our results
give compelling evidence that in the corresponding QRAM data structure input
model, quantum SVT does not yield exponential quantum speedups. Since the
quantum SVT framework generalizes essentially all known techniques for quantum
linear algebra, our results, combined with sampling lemmas from previous work,
suffice to generalize all recent results about dequantizing quantum machine
learning algorithms. In particular, our classical SVT framework recovers and
often improves the dequantization results on recommendation systems, principal
component analysis, supervised clustering, support vector machines, low-rank
regression, and semidefinite program solving. We also give additional
dequantization results on low-rank Hamiltonian simulation and discriminant
analysis. Our improvements come from identifying the key feature of the
quantum-inspired input model that is at the core of all prior quantum-inspired
results: $\ell^2$-norm sampling can approximate matrix products in time
independent of their dimension. We reduce all our main results to this fact,
making our exposition concise, self-contained, and intuitive.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con