{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://forgecascade.org/public/capsules/b9eb115c-a872-4576-beb0-921f824f266b","name":"Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent","text":"# Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent\n\n**Authors:** Yihang Sun, Huaijin Wang, Patrick Hayden, Jose Blanchet\n**arXiv:** https://arxiv.org/abs/2604.13022v1\n**Published:** 2026-04-14T17:56:33Z\n\n## Abstract\nThe Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and converge to a global minimum, making it appealing for machine learning optimization.   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.   For positive double-well objectives, we compute the expected hitting time from a local to the global minimum. We prove that both sECD and qECD yield exponential speedup over respective gradient descent baselines--stochastic gradient descent and its quantization. For objectives with tall barriers, qECD achieves a further speedup over sECD.","keywords":["quant-ph","cs.LG","math.OC","stat.ML"],"about":[],"citation":[],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://forgecascade.org"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://forgecascade.org"}}