量子极端学习机何时能取代量子储层？
When Can Quantum Extreme Learning Machines Replace Quantum Reservoirs?
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- QAR-Lab , Department of Computer Science Ludwig-Maximilians-Universit\"at M\"unchen (LMU Munich) , Munich, Germany
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中文总结 AI 辅助
本文研究量子极端学习机（QELMs）何时能取代量子储层计算机（QRCs），发现足够表达能力的QELMs在窗口增长且过去影响可忽略时可近似储层输出，但无法恢复未接收的过去信息。
中文摘要 AI 辅助
量子储层计算机（QRCs）保留来自早期输入的信息，而重置窗口量子极端学习机（QELMs）则重新开始，仅接收最近的一个输入窗口。我们确定了该窗口何时能取代储层的记忆。在我们所述的假设下，且使用精确期望值，当被忽略的过去的影响变得一致可忽略时，足够表达能力的QELMs可以随着其窗口的增长而任意精确地重现储层输出。然而，更长的窗口并不总能解决问题。我们构建了一个简单的两比特储层，它能精确执行时间回忆，而每个固定窗口预测器在无界延迟上都面临相同的正最坏情况误差，无论模型容量如何。分析基准和模拟区分了缺失历史与有限特征及有限测量。核心结论很简单：更好的表示可以改进对可用信息的利用，但无法恢复模型从未接收到的过去。
英文摘要
Quantum reservoir computers (QRCs) retain information from earlier inputs, whereas reset-window quantum extreme learning machines (QELMs) start afresh and receive only a recent input window. We establish when this window can replace the reservoir's memory. Under our stated assumptions and with exact expectation values, sufficiently expressive QELMs can reproduce reservoir outputs arbitrarily accurately as their windows grow precisely when the influence of the omitted past becomes uniformly negligible. However, longer windows do not always solve the problem. We construct a simple two-qubit reservoir that performs temporal recall exactly, while every fixed-window predictor faces the same positive worst-case error over unbounded delays, regardless of model capacity. Analytical benchmarks and simulations distinguish missing history from limited features and finite measurements. The central conclusion is simple: better representations can improve how available information is used, but cannot recover a past the model never receives.
