{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://froggit.ai/public/capsules/b9eb115c-a872-4576-beb0-921f824f266b","identifier":"b9eb115c-a872-4576-beb0-921f824f266b","url":"https://froggit.ai/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\nSource-backed public reference for arXiv:2604.13022.\n\n**Authors:** Yihang Sun, Huaijin Wang, Patrick Hayden, Jose Blanchet\n**Primary source:** https://arxiv.org/abs/2604.13022\n**Published:** 2026-04-14T17:56:33Z\n**Updated:** 2026-04-14T17:56:33Z\n**Categories:** quant-ph, cs.LG, math.OC, stat.ML\n\n## Abstract Summary\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.\n\n## Public Use Notes\n- This capsule summarizes the paper's arXiv metadata and abstract; it is not an independent replication or endorsement of the paper's claims.\n- Use it as a cited research reference for discovery, retrieval, and agent context.\n- For clinical, security, operational, or deployment-sensitive topics, treat the paper as research context rather than medical, legal, safety, or engineering advice.\n\n## Source\n- https://arxiv.org/abs/2604.13022","keywords":["quant-ph","cs.LG","math.OC","stat.ML"],"about":[],"citation":["https://arxiv.org/abs/2604.13022"],"isPartOf":{"@type":"Dataset","name":"Forge Cascade Knowledge Graph","url":"https://froggit.ai"},"publisher":{"@type":"Organization","name":"Forge Cascade","url":"https://froggit.ai"},"dateCreated":"2026-04-15T06:00:04.585000Z","dateModified":"2026-06-19T14:20:13Z","isBasedOn":"https://arxiv.org/abs/2604.13022","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":40},{"@type":"PropertyValue","name":"verification_status","value":"sources_verified"},{"@type":"PropertyValue","name":"provenance_status","value":"valid"},{"@type":"PropertyValue","name":"evidence_level","value":"primary_source"},{"@type":"PropertyValue","name":"content_hash","value":"45102e4480ba00b93e261ffbb1b338fa2e6e4b0b514539aeedbf200a9bd20a17"}]}