arXiv：cs.LG· Yihang Sun, Huaijin Wang, Patrick Hayden, Jose Blanchet·· 5 小时前AI 评分37
ECD 如何为不可微优化带来经典与量子加速：sECD 与 qECD 的首次解析研究
Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent
AI 导读
研究首次对能量守恒下降（ECD）进行解析分析，形式化了带能量守恒噪声的随机 ECD（sECD）动力学及 ECD 哈密顿量的量子版本（qECD）。在一维双井目标的 under-guessing 区间，sECD 与 qECD 的连续命中时间相对 SGD 和量子隧穿行走（QTW）均呈指数级改进；高势垒目标下 qECD 命中时间进一步优于 sECD。
正文
Abstract:We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation in a tractable model where the barrier-crossing mechanism can be computed explicitly. For one-dimensional double-well objectives in the under-guessing regime, we compute the expected dynamical hitting times from a local minimum to the global minimum. We prove that both sECD and qECD exhibit exponential improvements in continuous hitting time relative to their respective gradient-based baselines, stochastic gradient descent (SGD) and quantum tunneling walk (QTW). For objectives with tall barriers, qECD admits a further hitting time improvement over sECD. Mechanistically, ECD sidesteps the exponential cost associated with rare-escape events of SGD from local minima by moving from dissipative to energy-conserving dynamics.
| Comments: | 32 pages, 3 figures |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML) |
| Cite as: | arXiv:2604.13022 [quant-ph] |
| (or arXiv:2604.13022v2 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2604.13022 arXiv-issued DOI via DataCite |
Submission history
From: Yihang Sun [view email]
[v1]
Tue, 14 Apr 2026 17:56:33 UTC (104 KB)
[v2]
Thu, 1 Oct 2026 18:34:36 UTC (635 KB)
来源：arXiv：cs.LG · arxiv.org