Stochastic Quantum Hamiltonian Descent

• URL: http://arxiv.org/abs/2507.15424v1
• Date: Mon, 21 Jul 2025 09:24:49 GMT
• Title: Stochastic Quantum Hamiltonian Descent
• Authors: Sirui Peng, Shengminjie Chen, Xiaoming Sun, Hongyi Zhou,
• Abstract summary: We introduce Quantum Hamiltonian Descent (SQHD), a quantum optimization algorithm that integrates computational efficiency of methods with global exploration power of quantum dynamics.<n>We also propose a discrete-time gate gate that approximates dynamics while direct Lindbladian simulation, enabling these objectives on near-term quantum devices.
• Score: 5.8172845753874896
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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