Computationally efficient zero-noise extrapolation for quantum-gate-error mitigation

Abstract

Zero-noise extrapolation (ZNE) is a widely used technique for gate-error mitigation on near-term quantum computers because it can be implemented in software and does not require knowledge of the quantum computer noise parameters. Traditional ZNE requires a significant resource overhead in terms of quantum operations. A recent proposal using a targeted (or random) instead of fixed identity insertion method (RIIM versus FIIM) requires significantly fewer quantum gates for the same formal precision. We start by showing that RIIM can allow for ZNE to be deployed on deeper circuits than FIIM but requires many more measurements to achieve the same level of statistical uncertainty. We develop two extensions to FIIM and RIIM. The list identity insertion method allows us to mitigate the error from certain controlled-not (cnot) gates, typically those with the largest error. The set identity insertion method naturally interpolates between the measurement-efficient FIIM and the gate-efficient RIIM, allowing us to trade off fewer cnot gates for more measurements. Finally, we investigate a way to boost the number of measurements, namely, to run ZNE in parallel, utilizing as many quantum devices as are available. We explore the performance of RIIM in a parallel setting where there is a nontrivial spread in noise across sets of qubits within or across quantum computers.