BBGKY hierarchy for quantum error mitigation

TL;DR

This paper introduces a novel quantum error mitigation method leveraging the BBGKY hierarchy to improve measurement accuracy in noisy quantum simulations, demonstrating significant error reduction on the lattice Schwinger model.

Contribution

The authors develop a new error mitigation scheme based on the BBGKY hierarchy integrated with ZNE, ensuring polynomial scaling and improved accuracy in quantum simulations.

Findings

Error reduction of approximately 18% for particle number measurements.

Error reduction of approximately 53% for charge measurements.

Method tested successfully on noisy quantum simulations of the lattice Schwinger model.

Abstract

Mitigation of quantum errors is critical for current NISQ devices. In the present work, we address this task by treating the execution of quantum algorithms as the time evolution of an idealized physical system. We use knowledge of its physics to assist the mitigation of the quantum noise produced on the real device. In particular, the time evolution of the idealized system obeys a corresponding BBGKY hierarchy of equations. This is the basis for the novel error mitigation scheme that we propose. Specifically, we employ a subset of the BBGKY hierarchy as supplementary constraints in the ZNE method for error mitigation. We ensure that the computational cost of the scheme scales polynomially with the system size. We test our method on digital quantum simulations of the lattice Schwinger model under noise levels mimicking realistic quantum hardware. We demonstrate that our scheme systematically improves the error mitigation for the measurements of the particle number and the charge within this system. Relative to ZNE we obtain an average reduction of the error by $(18.2 \pm 0.5)\%$ and $(52.8 \pm 6.3)\%$ for the respective above observables. We propose further applications of the BBGKY hierarchy for quantum error mitigation.