Matchgate quantum computing and non-local process analysis

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 single-photon linear optics experiment. The gate performance is 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 non-local two-qubit unitaries. We propose the nonlocal distance-which is independent of local imperfections such as uncorrelated noise or uncompensated local rotations-as a new diagnostic process measure for the non-local properties of the implemented gate.