Simplifying errors by symmetry and randomisation

Abstract

We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error channel is analysed; these results are then generalised to multiple error channels. Error simplification for each method is shown to be either constant, linear, or exponential in terms of system size. Finally, example applications are provided, along with experiments run on superconducting quantum hardware and numerical simulation. These applications are: (1) reducing the sample complexity of matrix-inversion measurement error mitigation by error symmetrisation, (2) improving the effectiveness of noise-estimation circuit error mitigation by error randomisation, and (3) improving the predictability of noisy circuit performance by error randomisation.