## 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 language | English |
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Pages (from-to) | 809-830 |

Number of pages | 22 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 466 |

Issue number | 2115 |

DOIs | |

State | Published - 8 Mar 2010 |

Externally published | Yes |

## Keywords

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