arXiv：cs.LG· Mikhail Mints, Eric R. Anschuetz·· 5 小时前AI 评分43
量子神经网络可高效学习碎片化分类
Fragmentation is Efficiently Learnable by Quantum Neural Networks
AI 导读
研究提出"碎片分类"学习问题：给定量子态输入，判断其属于哪个低维动力学不相连子空间，并证明在碎片化现象满足特定条件时，量子计算机可高效求解该问题。作者进一步证明已知去量子化技术对碎片分类失效，为该任务的经典计算难度提供证据。这是罕见的物理动机量子机器学习任务，既对量子计算机高效，又无已知经典去量子化方案。
正文
Abstract:In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.
| Comments: | 32 pages, 5 figures |
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2512.00751 [quant-ph] |
| (or arXiv:2512.00751v4 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2512.00751 arXiv-issued DOI via DataCite |
Submission history
From: Mikhail Mints [view email]
[v1]
Sun, 30 Nov 2025 06:04:58 UTC (166 KB)
[v2]
Tue, 2 Dec 2025 16:57:47 UTC (166 KB)
[v3]
Thu, 7 May 2026 03:25:02 UTC (52 KB)
[v4]
Thu, 1 Oct 2026 19:50:33 UTC (126 KB)
来源：arXiv：cs.LG · arxiv.org