Classically propagating noise for faster error mitigation

Quantum error mitigation can enable noisy quantum processors to produce unbiased estimates of observable expectation values, at a runtime cost exponential in the noise rate. Novel error mitigation methods have emerged that leverage classical compute resources to reduce error mitigation overhead, at the expense of classical runtime and controlled error. Pauli propagation has gained interest for classically simulating certain problems such as near-Clifford circuits, and can naturally leverage the sparsity of Pauli-based noise models. Here, we present a hybrid workflow for Pauli propagation that relies on the forward propagation of inverse noise channels classically, and the measurement of a modified observable on a quantum computer. We study the validity and viability of such classical Pauli propagation for error mitigation, including numerical and experimental results, and open-source software tools.