Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Quantum Algorithm for Solving Linear Differential Equations: Theory
  and Experiment   We present and experimentally realize a quantum algorithm for efficiently
solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an
$N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector
$\textbf{\emph{x}}(0)$, obtain a target vector $\textbf{\emph{x}}(t)$ as a
function of time $t$ according to the constraint
$d\textbf{\emph{x}}(t)/dt=\mathcal{M}\textbf{\emph{x}}(t)+\textbf{\emph{b}}$.
We show that our algorithm exhibits an exponential speedup over its classical
counterpart in certain circumstances. In addition, we demonstrate our quantum
algorithm for a $4\times4$ linear differential equation using a 4-qubit nuclear
magnetic resonance quantum information processor. Our algorithm provides a key
technique for solving many important problems which rely on the solutions to
linear differential equations.

37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex