Matchgate and space-bounded quantum computations are equivalent

Richard Jozsa, Barbara Kraus, Akimasa Miyake, John Watrous

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

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 characterize their power as coinciding with polynomial-time and logarithmic-space-bounded universal unitary quantum computation.

Original languageEnglish
Pages (from-to)809-830
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume466
Issue number2115
DOIs
StatePublished - 8 Mar 2010
Externally publishedYes

Keywords

  • Quantum computational complexity
  • Quantum matchgates
  • Space-bounded computation

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