Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum-inspired algorithms for multivariate analysis: from
  interpolation to partial differential equations   In this work we study the encoding of smooth, differentiable multivariate
functions in quantum registers, using quantum computers or tensor-network
representations. We show that a large family of distributions can be encoded as
low-entanglement states of the quantum register. These states can be
efficiently created in a quantum computer, but they are also efficiently
stored, manipulated and probed using Matrix-Product States techniques. Inspired
by this idea, we present eight quantum-inspired numerical analysis algorithms,
that include Fourier sampling, interpolation, differentiation and integration
of partial derivative equations. These algorithms combine classical ideas --
finite-differences, spectral methods -- with the efficient encoding of quantum
registers, and well known algorithms, such as the Quantum Fourier Transform.
{When these heuristic methods work}, they provide an exponential speed-up over
other classical algorithms, such as Monte Carlo integration, finite-difference
and fast Fourier transforms (FFT). But even when they don't, some of these
algorithms can be translated back to a quantum computer to implement a similar
task.

3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph