Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Fourier analysis for multivariate functions and applications to
  a class of Schr\"odinger-type partial differential equations   In this work, we develop a highly efficient representation of functions and
differential operators based on Fourier analysis. Using this representation, we
create a variational hybrid quantum algorithm to solve static,
Schr\"odinger-type, Hamiltonian partial differential equations (PDEs), using
space-efficient variational circuits, including the symmetries of the problem,
and global and gradient-based optimizers. We use this algorithm to benchmark
the performance of the representation techniques by means of the computation of
the ground state in three PDEs, i.e., the one-dimensional quantum harmonic
oscillator, and the transmon and flux qubits, studying how they would perform
in ideal and near-term quantum computers. With the Fourier methods developed
here, we obtain low infidelities of order $10^{-4}-10^{-5}$ using only three to
four qubits, demonstrating the high compression of information in a quantum
computer. Practical fidelities are limited by the noise and the errors of the
evaluation of the cost function in real computers, but they can also be
improved through error mitigation techniques.

6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics