Quantum error mitigation by hierarchy-informed sampling: chiral dynamics in the Schwinger model

TL;DR

This paper introduces a hierarchy-informed sampling method for quantum error mitigation on NISQ devices, effectively reducing noise in simulations of the Schwinger model's chiral magnetic effect.

Contribution

It presents a novel error mitigation scheme using BBGKY hierarchy equations applicable to time-dependent Hamiltonian simulations on NISQ hardware.

Findings

Effective noise reduction in quantum simulations of the Schwinger model.

Systematic improvement of mitigation with more BBGKY constraints.

Polynomial resource overhead for favorable Hamiltonians.

Abstract

Quantum simulations on current NISQ hardware are limited by its noisy nature, making efficient quantum error mitigation methods highly demanded. In this paper we introduce a novel mitigation scheme, applicable to arbitrary quantum simulations of time-dependent Hamiltonian dynamics on NISQ devices. The scheme uses a polynomial subset of extended qubit Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations as a sampling criterion of possible mitigated candidates for the quantum observables. We show that for favorable Hamiltonians the polynomial subset of BBGKY hierarchy equations leads to a polynomial overhead in both classical and quantum resources. We employ the method to mitigate simulations of the chiral magnetic effect (CME), a chiral feature of the Schwinger model. We empirically show the effectiveness of our scheme at recovering the real-time dynamics of the CME from noisy quantum simulations of the Schwinger model, for a range of different parameter values of the model. We numerically demonstrate a systematic reduction of quantum noise, together with an increasing noise reduction capability as the amount of BBGKY constraints grows.