A quantum-classical performance separation in nonconvex optimization

Jiaqi Leng; Yufan Zheng; Xiaodi Wu

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arXiv · 2311.00811

A quantum-classical performance separation in nonconvex optimization

Jiaqi Leng·Yufan Zheng·Xiaodi Wu

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Abstract

In this paper, we identify a family of nonconvex continuous optimization instances, each $d$-dimensional instance with $2^d$ local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently proposed Quantum Hamiltonian Descent (QHD) algorithm [Leng et al., arXiv:2303.01471] is able to solve any $d$-dimensional instance from this family using $\widetilde{\mathcal{O}}(d^3)$ quantum queries to the function value and $\widetilde{\mathcal{O}}(d^4)$ additional 1-qubit and 2-qubit elementary quantum gates. On the other side, a comprehensive empirical study suggests that representative state-of-the-art classical optimization algorithms/solvers (including Gurobi) would require a super-polynomial time to solve such optimization instances.

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Jiaqi Leng, Yufan Zheng, Xiaodi Wu. 2023-11-01. A quantum-classical performance separation in nonconvex optimization. https://arxiv.org/abs/2311.00811

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