arXiv：cs.LG（机器学习，全量分类）· Yibin Wang·· 15 小时前AI 评分30
有限记忆量子过程的序列容量研究
Sequential Capacity of Quantum Processes with Finite Memory
AI 导读
研究量化了固定内部记忆的量子设备随运行时间增长的响应复杂度，提出"序列容量"概念：在固定分辨率和系统规模下，容量随每轮时间步数K以K log K量级增长，而经典随机过程仅呈线性增长。该构造通过单个可见量子比特上的时变相位旋转实现，无需额外内部记忆，测试响应概率恰为0或1。研究进一步证明，在弱残余相位噪声下，逆残余相位翻转概率决定了限制对数增长增强的相干时间尺度。
正文
Abstract:How complex can the responses of a quantum device become as it runs longer with a fixed internal memory? We quantify this complexity through sequential response capacity: how many adaptive testing stages, each using a fresh run, can continue to separate possible processes by a prescribed gap in response probabilities. For fixed system and memory sizes, we establish a tight law relating this capacity to run length and probability resolution. At fixed resolution, the capacity grows on the order of $K\log K$, where $K$ is the number of time steps in each run. Our construction attains this growth using time-dependent phase rotations on a single visible qubit with no additional internal memory; its tests give response probabilities exactly zero or one. Under the same tests, classical stochastic processes that measure in a fixed basis at every step have only linear capacity at fixed sizes and resolution. For phase sequences selected by a stored classical label, we then quantify how known independent Pauli noise changes this logarithmic enhancement. With ideal controls and weak residual phase noise after correction, we prove matching capacity bounds at a fixed small probability gap. These bounds identify the inverse residual phase-flip probability as the coherence timescale that limits the extra logarithmic growth.
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.02068 [quant-ph] |
| (or arXiv:2610.02068v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02068 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yibin Wang [view email]
[v1]
Thu, 1 Oct 2026 17:08:19 UTC (71 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org