Matchgate and space-bounded quantum computations are equivalent
Abstract
Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. We show that the computational power of circuits of matchgates is equivalent to that of space-bounded quantum computation with unitary gates, with space restricted to being logarithmic in the width of the matchgate circuit. In particular, for the conventional setting of polynomial-sized (logarithmic-space generated) families of matchgate circuits, known to be classically simulatable, we characterise their power as coinciding with polynomial-time and logarithmic-space bounded universal unitary quantum computation.
Cite
@article{arxiv.0908.1467,
title = {Matchgate and space-bounded quantum computations are equivalent},
author = {Richard Jozsa and Barbara Kraus and Akimasa Miyake and John Watrous},
journal= {arXiv preprint arXiv:0908.1467},
year = {2010}
}
Comments
22 pages