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arXiv · 2507.15424

Stochastic Quantum Hamiltonian Descent

Sirui Peng·Shengminjie Chen·Xiaoming Sun·Hongyi Zhou
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Abstract

Stochastic Gradient Descent (SGD) and its variants underpin modern machine learning by enabling efficient optimization of large-scale models. However, their local search nature limits exploration in complex landscapes. In this paper, we introduce Stochastic Quantum Hamiltonian Descent (SQHD), a quantum optimization algorithm that integrates the computational efficiency of stochastic gradient methods with the global exploration power of quantum dynamics. We propose a Lindbladian dynamics as the quantum analogue of continuous-time SGD. We further propose a discrete-time gate-based algorithm that approximates these dynamics while avoiding direct Lindbladian simulation, enabling practical implementation on near-term quantum devices. We rigorously prove the convergence of SQHD for convex and smooth objectives. Numerical experiments demonstrate that SQHD also exhibits advantages in non-convex optimization. All these results highlight its potential for quantum-enhanced machine learning.

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Sirui Peng, Shengminjie Chen, Xiaoming Sun, Hongyi Zhou. 2025-07-21. Stochastic Quantum Hamiltonian Descent. https://arxiv.org/abs/2507.15424

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