Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems

• URL: http://arxiv.org/abs/2309.08120v3
• Date: Sun, 7 Apr 2024 12:48:53 GMT
• Title: Post-processing variationally scheduled quantum algorithm for constrained combinatorial optimization problems
• Authors: Tatsuhiko Shirai, Nozomu Togawa,
• Abstract summary: We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained optimization problems (COPs) pVSQA combines the variational methods and the post-processing technique. We implement pVSQA on a quantum annealer and a gate-type quantum device.
• Score: 6.407238428292173
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-type quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-type quantum device. The experimental results demonstrate the effectiveness of our proposed method.

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