Credibility of noisy intermediate-scale quantum computers

The value of quantum computers and simulators lie in solving efficiently and correctly problems that are hard classically. This is particularly relevant for simulation, sampling, and optimisation problems whose solutions cannot be verified efficiently classically, unlike integer factoring. I will present methods that can provide, for a given problem, an upper bound on the variation distance between an experimentally obtained output from a noisy quantum computer and the ideal output from a noiseless device. I will show how this can be achieved without the inherently infeasible method of simulating the quantum computation classically. I will highlight the vital interplay between empirical experimental observations and mathematical assumptions. I will conclude with some applications on judging the credibility of trusting noisy intermediate-scale quantum computers in simulating hard condensed-matter physics problems.