Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries

• Published in: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) pp. 291 - 300
• Main Authors: Shaydulin, Ruslan, Galda, Alexey
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.10.2021
• Subjects: Approximation algorithms; Conferences; Error analysis; error mitigation; Linear programming; Logic gates; Quantum Approximate Optimization Algorithm; quantum computing; quantum optimization; Quantum state; Qubit
• DOI: 10.1109/QCE52317.2021.00046

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.