Optimization via Quantum Preconditioning

• URL: http://arxiv.org/abs/2502.18570v1
• Date: Tue, 25 Feb 2025 19:00:41 GMT
• Title: Optimization via Quantum Preconditioning
• Authors: Maxime Dupont, Tina Oberoi, Bhuvanesh Sundar,
• Abstract summary: We introduce a quantum preconditioning approach based on the quantum approximate optimization.<n>It transforms the input problem into a more suitable form for a solver with the level of preconditioning determined by the depth of the quantum circuit.<n>We demonstrate that best-in-class classical algorithms can converge more rapidly when given quantum preconditioned input for various problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It transforms the input problem into a more suitable form for a solver with the level of preconditioning determined by the depth of the quantum circuit. We demonstrate that best-in-class classical heuristics such as simulated annealing and the Burer-Monteiro algorithm can converge more rapidly when given quantum preconditioned input for various problems, including Sherrington-Kirkpatrick spin glasses, random 3-regular graph maximum-cut problems, and a real-world grid energy problem. Accounting for the additional time taken for preconditioning, the benefit offered by shallow circuits translates into a practical quantum-inspired advantage for random 3-regular graph maximum-cut problems through quantum circuit emulations. We investigate why quantum preconditioning makes the problem easier and test an experimental implementation on a superconducting device. We identify challenges and discuss the prospects for a hardware-based quantum advantage in optimization via quantum preconditioning.

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