Matchgate quantum computing and non-local process analysis

TL;DR

This paper demonstrates the decomposition, implementation, and characterization of matchgate quantum gates in linear optics, introducing a novel fidelity map and non-local distance for analyzing non-local quantum processes.

Contribution

It provides a simple decomposition method for matchgates, implements them experimentally with photons, and introduces new tools for analyzing their non-local properties.

Findings

Successful implementation of matchgates in linear optics

Introduction of a fidelity map for nonlocal unitaries

Proposal of a non-local distance as a diagnostic measure

Abstract

In the circuit model, quantum computers rely on the availability of a universal quantum gate set. A particularly intriguing example is a set of two-qubit only gates: matchgates, along with SWAP (the exchange of two qubits). In this paper, we show a simple decomposition of arbitrary matchgates into better known elementary gates, and implement a matchgate in a linear-optics experiment using single photons. The gate performance was fully characterized via quantum process tomography. Moreover, we represent the resulting reconstructed quantum process in a novel way, as a fidelity map in the space of all possible nonlocal two-qubit unitaries. We propose the non-local distance - which is independent of local imperfections like uncorrelated noise or uncompensated local rotations - as a new diagnostic process measure for the non-local properties of the implemented gate.