Geometries for universal quantum computation with matchgates

TL;DR

This paper explores alternative geometries enabling universal quantum computation using only matchgates with nearest-neighbor interactions, expanding potential architectures beyond linear chains.

Contribution

It introduces new geometries that achieve universality with matchgates, beyond the standard linear chain configuration.

Findings

Certain geometries enable universal quantum computation with matchgates.

Matchgates remain classically simulatable on a chain but become universal with alternative geometries.

New architectures for quantum computers relying solely on matchgates are proposed.

Abstract

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