Optimization via Quantum Preconditioning

TL;DR

This paper introduces a quantum preconditioning method using the quantum approximate optimization algorithm to transform problems into more solvable forms, demonstrating improved classical solver convergence and potential quantum advantage.

Contribution

It presents a novel quantum preconditioning technique that enhances classical optimization algorithms and explores its practical implementation and advantages.

Findings

Quantum preconditioning accelerates classical solver convergence.

Shallow quantum circuits can provide practical quantum-inspired advantages.

Experimental implementation on superconducting hardware demonstrates feasibility.

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.