Extending matchgates into universal quantum computation

Details Extending matchgates into universal quantum computation Extending matchgates into universal quantum computation

2011-06-09

arxiv.org/abs/1106.1863v1

Phys. Rev. A 84, 022310 (2011)

Physics

Quantum Physics

9 pages, 2 figures

Scientific paper

10.1103/PhysRevA.84.022310

Matchgates are a family of two-qubit gates associated with noninteracting fermions. They are classically simulatable if acting only on nearest neighbors, but become universal for quantum computation if we relax this restriction or use SWAP gates [Jozsa and Miyake, Proc. R. Soc. A 464, 3089 (2008)]. We generalize this result by proving that any nonmatchgate parity-preserving unitary is capable of extending the computational power of matchgates into universal quantum computation. We identify the single local invariant of parity-preserving unitaries responsible for this, and discuss related results in the context of fermionic systems.

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