Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries

TL;DR

This paper presents a symmetry-based error mitigation technique for QAOA, improving fidelity and solution accuracy on near-term quantum devices by projecting states into symmetry-restricted subspaces, demonstrated on IBM hardware.

Contribution

The paper introduces a novel symmetry-based error mitigation method for QAOA that enhances fidelity and solution quality, applicable to various objective functions with symmetries.

Findings

23% average improvement in quantum state fidelity with symmetry projection

Effective error mitigation demonstrated on IBM Quantum processor with up to 5 qubits

Method applicable to any symmetric objective function and generalized QAOA variants

Abstract

High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an application-specific approach for mitigating the errors in QAOA evolution by leveraging the symmetries present in the classical objective function to be optimized. Specifically, the QAOA state is projected into the symmetry-restricted subspace, with projection being performed either at the end of the circuit or throughout the evolution. Our approach improves the fidelity of the QAOA state, thereby increasing both the accuracy of the sample estimate of the QAOA objective and the probability of sampling the binary string corresponding to that objective value. We demonstrate the efficacy of the proposed methods on QAOA applied to the MaxCut problem, although our methods are general and apply to any objective function with symmetries, as well as to the generalization of QAOA with alternative mixers. We experimentally verify the proposed methods on an IBM Quantum processor, utilizing up to 5 qubits. When leveraging a global bit-flip symmetry, our approach leads to a 23% average improvement in quantum state fidelity.