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arXiv · 0908.1467

Matchgate and space-bounded quantum computations are equivalent

Richard Jozsa·Barbara Kraus·Akimasa Miyake·John Watrous
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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.

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Richard Jozsa, Barbara Kraus, Akimasa Miyake, John Watrous. 2010-01-30. Matchgate and space-bounded quantum computations are equivalent. https://doi.org/10.1098/rspa.2009.0433

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