On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks

Author name not available (Why is that?)

Publication date: 28 September 2022

Abstract: Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima. We show that QTW achieves quantum speedup over classical stochastic gradient descents (SGD) when the barriers between different local minima are high but thin and the minima are flat. Based on this observation, we construct a specific double-well landscape, where classical algorithms cannot efficiently hit one target well knowing the other well but QTW can when given proper initial states near the known well. Finally, we corroborate our findings with numerical experiments.

Has companion code repository: https://github.com/liuyz0/quantum-tunneling

This page was built for publication: On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6412310)