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. This 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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• NP-hard problems
• Optimization problems
• Quantum algorithms
• Quantum benchmarking
• Quantum circuits
• Spin glasses
• Superconducting qubits
• Ising model