Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The computational power of matchgates and the XY interaction on
  arbitrary graphs   Matchgates are a restricted set of two-qubit gates known to be classically
simulable when acting on nearest-neighbor qubits on a path, but universal for
quantum computation when the qubits are arranged on certain other graphs. Here
we characterize the power of matchgates acting on arbitrary graphs.
Specifically, we show that they are universal on any connected graph other than
a path or a cycle, and that they are classically simulable on a cycle. We also
prove the same dichotomy for the XY interaction, a proper subset of matchgates
related to some implementations of quantum computing.

7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio