Optimizer-aware Circuit Design for Error Unfolding in Variational Quantum Eigensolver

Quantum hardware suffers from errors and any measured output is thus a convolution of the intended result and some error distribution. The Variational Quantum Eigensolver has a classical optimizer step that takes the output from the quantum chip to determine the input parameters for the next iteration. Errors can prevent the optimizer from making progress; and if they are too large, make it impossible to calculate, let alone find, the global minimum. If the error distribution were known, it could be unfolded, but this is generally not the case, especially if the errors do not commute with the whole circuit. Exploiting ideas from randomized compilation, we introduce twirl gates into the circuit, generating logically equivalent circuits with the same number of gates and same output, but with different error behavior. The physical processes do not change, thus error rates remain the same as well. Using a Markov chain as error model, we apply a maximum likelihood fit to find those rates that produce migration matrices for unfolding consistent with all observed distributions. This results in improved output estimates of the quantum computer, and better defined uncertainties as input to the classical optimizer leading to faster convergence and a more robustly defined global minimum.