Estimating distinguishability measures on quantum computers

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result from ideal case. most prominent are those based on fidelity and trace distance, due to their physical interpretations. In this paper, we propose review several algorithms for estimating distance fidelity. can be used distinguishing states, channels, strategies (the last also known in literature as "quantum combs"). fidelity-based offer novel interpretations these terms maximum probability with which single prover (or competing provers) convince verifier accept outcome an associated computation. We simulate many using variational approach parameterized circuits. find simulations converge well both noiseless noisy scenarios, all examples considered. Furthermore, exhibit parameter noise resilience. Finally, establish strong relationship between various computational complexity classes estimation problems.