Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simulating quantum computation by contracting tensor networks   The treewidth of a graph is a useful combinatorial measure of how close the
graph is to a tree. We prove that a quantum circuit with $T$ gates whose
underlying graph has treewidth $d$ can be simulated deterministically in
$T^{O(1)}\exp[O(d)]$ time, which, in particular, is polynomial in $T$ if
$d=O(\log T)$. Among many implications, we show efficient simulations for
log-depth circuits whose gates apply to nearby qubits only, a natural
constraint satisfied by most physical implementations. We also show that
one-way quantum computation of Raussendorf and Briegel (Physical Review
Letters, 86:5188--5191, 2001), a universal quantum computation scheme with
promising physical implementations, can be efficiently simulated by a
randomized algorithm if its quantum resource is derived from a small-treewidth
graph.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci