Recursive Quantum Relaxation for Combinatorial Optimization Problems

• URL: http://arxiv.org/abs/2403.02045v2
• Date: Tue, 19 Mar 2024 03:07:39 GMT
• Title: Recursive Quantum Relaxation for Combinatorial Optimization Problems
• Authors: Ruho Kondo, Yuki Sato, Rudy Raymond, Naoki Yamamoto,
• Abstract summary: We show that some existing quantum optimization methods can be unified into a solver that finds the binary solution that is most likely measured from the optimal quantum state. Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO outperforms the Goemans--Williamson method and is comparable to state-of-the-art classical solvers.
• Score: 3.3053321430025258
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper shows that some existing quantum optimization methods can be unified into a solver that finds the binary solution that is most likely measured from the optimal quantum state. Combining this finding with the concept of quantum random access codes (QRACs) for encoding bits into quantum states on fewer qubits, we propose an efficient recursive quantum relaxation method called recursive quantum random access optimization (RQRAO) for MAX-CUT. Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO outperforms the Goemans--Williamson method and is comparable to state-of-the-art classical solvers. The codes will be made available soon.

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