Matchgate and space-bounded quantum computations are equivalent

Details Matchgate and space-bounded quantum computations are equivalent Matchgate and space-bounded quantum computations are equivalent

2009-08-11

arxiv.org/abs/0908.1467v2

Proc. R. Soc. A 466, 809-830 (2010)

Physics

Quantum Physics

22 pages

Scientific paper

10.1098/rspa.2009.0433

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.

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