Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation

TL;DR

This paper introduces new methods to improve zero noise extrapolation (ZNE) for quantum error mitigation, reducing resource overhead and enabling deeper circuit execution by optimizing measurement strategies and parallelizing ZNE across multiple quantum devices.

Contribution

It proposes extensions to existing ZNE techniques, including LIIM and SIIM, and explores parallel ZNE to enhance efficiency and scalability on noisy quantum hardware.

Findings

RIIM allows deeper circuits but requires more measurements.

LIIM effectively mitigates errors from high-error CNOT gates.

Parallel ZNE improves measurement efficiency across multiple devices.

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 maintain the same statistical uncertainty. We develop two extensions to FIIM and RIIM. The List Identity Insertion Method (LIIM) allows to mitigate the error from certain CNOT gates, typically those with the largest error. Set Identity Insertion Method (SIIM) naturally interpolates between the measurement-efficient FIIM and the gate-efficient RIIM, allowing 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 non-trivial spread in noise across sets of qubits within or across quantum computers.