Fast Convex Optimization with Quantum Gradient Methods
Abstract
We study quantum algorithms based on quantum (sub)gradient estimation using noisy function evaluation oracles, and demonstrate the first dimension-independent query complexities (up to poly-logarithmic factors) for zeroth-order convex optimization in both smooth and nonsmooth settings. Interestingly, only using noisy function evaluation oracles, we match the first-order query complexities of classical gradient descent, thereby exhibiting exponential separation between quantum and classical zeroth-order optimization. We then generalize these algorithms to work in non-Euclidean settings by using quantum (sub)gradient estimation to instantiate mirror descent and its variants, including dual averaging and mirror prox. By leveraging a connection between semidefinite programming and eigenvalue optimization, we use our quantum mirror descent method to give a new quantum algorithm for solving semidefinite programs, linear programs, and zero-sum games. We identify a parameter regime in which our zero-sum games algorithm is faster than any existing classical or quantum approach.
Cite
@article{arxiv.2503.17356,
title = {Fast Convex Optimization with Quantum Gradient Methods},
author = {Brandon Augustino and Dylan Herman and Enrico Fontana and Junhyung Lyle Kim and Jacob Watkins and Shouvanik Chakrabarti and Marco Pistoia},
journal= {arXiv preprint arXiv:2503.17356},
year = {2025}
}
Comments
Introduction has been restructured; the statements of Lemma 2.1, Theorem A.2 (Theorem 3.1 in v1), and Theorem D.3 (Theorem 5.3 in v1) are updated