Synergetic quantum error mitigation by randomized compiling and zero-noise extrapolation for the variational quantum eigensolver

We present a quantum error mitigation approach for the variational quantum eigensolver (VQE), demonstrating particular efficacy in addressing coherent noise. Our investigation reveals that even a small amount of coherent noise can produce considerable errors, which are difficult to suppress through conventional error mitigation techniques. The proposed error mitigation scheme offers a significant reduction in these errors by employing a synergistic combination of randomized compiling (RC) and zero-noise extrapolation (ZNE). This approach functions by utilizing RC to transform coherent noise into stochastic Pauli noise, which can then be predictively and effectively suppressed via ZNE. We provide numerical simulations of VQE applied to small molecular systems using the unitary coupled cluster ansatz with single and double excitations (UCCSD). Our findings show that the proposed strategy can effectively diminish energy errors induced by various forms of coherent noise (including over-rotation and crosstalk noise) by up to two orders of magnitude.