Alexander Dalzell: Random quantum circuits transform local noise into global white noise
0We examine the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We will show that, for local noise that is sufficiently weak and unital, the output distribution p_noisy of typical circuits can be approximated by F*p_ideal + (1−F)*p_unif, where F is the probability that no local errors occur, p_ideal is the distribution that would arise if there were no errors, and p_unif is the uniform distribution. In other words, local errors are scrambled by the random quantum circuit and contribute only white noise (uniform output). Importantly, we upper bound the total variation error (averaged over random circuit instance) in this approximation and show it grows with the square root of the number of error locations (rather than linearly). The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; it was an underlying assumption in complexity-theoretic arguments that low-fidelity random quantum circuits cannot be efficiently sampled classically. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.