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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.15424 |
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| _version_ | 1866916853684633600 |
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| author | Peng, Sirui Chen, Shengminjie Sun, Xiaoming Zhou, Hongyi |
| author_facet | Peng, Sirui Chen, Shengminjie Sun, Xiaoming Zhou, Hongyi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Quantum Hamiltonian Descent Peng, Sirui Chen, Shengminjie Sun, Xiaoming Zhou, Hongyi Quantum Physics 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. |
| title | Stochastic Quantum Hamiltonian Descent |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.15424 |