The computational power of matchgates and the XY interaction on arbitrary graphs
Quantum Physics
2018-08-02 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1308.1463,
title = {The computational power of matchgates and the XY interaction on arbitrary graphs},
author = {Daniel J. Brod and Andrew M. Childs},
journal= {arXiv preprint arXiv:1308.1463},
year = {2018}
}
Comments
10 pages, 6 figures