Gaining confidence on the correct realization of arbitrary quantum computations

TL;DR

This paper introduces verification protocols that leverage matchgate computations and classical simulation techniques to confidently verify the correct execution of any universal quantum computation, even with errors.

Contribution

It develops new verification protocols combining weak simulation, randomized compiling, and classical statistics for realistic quantum computation validation.

Findings

Protocols can verify arbitrary quantum computations.

Verification circuits resemble original circuits closely.

Effective even in the presence of errors.

Abstract

We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are classically efficiently simulable, become universal if supplemented with additional resources. We combine tools from weak simulation, randomized compiling, and classical statistics to derive verification circuits. These circuits have the property that (i) they strongly resemble the original circuit and (ii) cannot only be classically efficiently simulated in the ideal, i.e. error free, scenario, but also in the realistic situation where errors are present. In fact, in one of the protocols we apply exactly the same circuit as in the original computation, however, to a slightly modified input state.