Geometries for universal quantum computation with matchgates

摘要

Matchgates are a group of two-qubit gates associated with free fermions. They are classically simulatablenif restricted to act between nearest neighbors on a one-dimensional chain, but become universal for quantumncomputation with longer-range interactions. We describe various alternative geometries with nearest-neighborninteractions that result in universal quantum computation with matchgates only, including subtle departures fromnthe chain. Our results pave the way for new quantum computer architectures that rely solely on the simpleninteractions associated with matchgates.