Adiabatic-Passage-Based Parameter Setting for Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2312.00077v3
• Date: Mon, 22 Jan 2024 07:15:05 GMT
• Title: Adiabatic-Passage-Based Parameter Setting for Quantum Approximate Optimization Algorithm
• Authors: Mingyou Wu, Hanwu Chen
• Abstract summary: We propose a novel adiabatic-passage-based parameter setting method. This method remarkably reduces the optimization cost, specifically when applied to the 3-SAT problem, to a sublinear level.
• Score: 0.7252027234425334
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Approximate Optimization Algorithm (QAOA) exhibits significant potential for tackling combinatorial optimization problems. Despite its promise for near-term quantum devices, a major challenge in applying QAOA lies in the cost of circuit runs associated with parameter optimization. Existing methods for parameter setting generally incur at least a superlinear cost concerning the depth p of QAOA. In this study, we propose a novel adiabatic-passage-based parameter setting method that remarkably reduces the optimization cost, specifically when applied to the 3-SAT problem, to a sublinear level. Beginning with an analysis of the random model of the specific problem, this method applies a problem-dependent preprocessing on the problem Hamiltonian analytically, effectively segregating the magnitude of parameters from the scale of the problem. Consequently, a problem-independent initialization is achieved without incurring any optimization cost or pre-computation. Furthermore, the parameter space is adjusted based on the continuity of the optimal adiabatic passage, resulting in a reduction in the disparity of parameters between adjacent layers of QAOA. By leveraging this continuity, the cost to find quasi-optimal parameters is significantly reduced to a sublinear level.

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