Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster quantum-inspired algorithms for solving linear systems   We establish an improved classical algorithm for solving linear systems in a
model analogous to the QRAM that is used by quantum linear solvers. Precisely,
for the linear system $A\x = \b$, we show that there is a classical algorithm
that outputs a data structure for $\x$ allowing sampling and querying to the
entries, where $\x$ is such that $\|\x - A^{-1}\b\|\leq \epsilon \|A^{-1}\b\|$.
This output can be viewed as a classical analogue to the output of quantum
linear solvers. The complexity of our algorithm is $\widetilde{O}(\kappa_F^6
\kappa^2/\epsilon^2 )$, where $\kappa_F = \|A\|_F\|A^{-1}\|$ and $\kappa =
\|A\|\|A^{-1}\|$. This improves the previous best algorithm [Gily{\'e}n, Song
and Tang, arXiv:2009.07268] of complexity $\widetilde{O}(\kappa_F^6
\kappa^6/\epsilon^4)$. Our algorithm is based on the randomized Kaczmarz
method, which is a particular case of stochastic gradient descent. We also find
that when $A$ is row sparse, this method already returns an approximate
solution $\x$ in time $\widetilde{O}(\kappa_F^2)$, while the best quantum
algorithm known returns $\ket{\x}$ in time $\widetilde{O}(\kappa_F)$ when $A$
is stored in the QRAM data structure. As a result, assuming access to QRAM and
if $A$ is row sparse, the speedup based on current quantum algorithms is
quadratic.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th