用量子电路循环编码输入与反馈,提升时序预测精度。
Recurrent Quantum Feature Maps for Reservoir Computing
- 用固定量子电路循环处理当前输入和历史输出反馈
- 在Mackey-Glass任务上误差低于经典模型,且所需量子资源少
- 对噪声鲁棒但对双量子比特门误差敏感,适合近中期量子硬件
储层计算为处理大量时序数据提供了一种快速方法,其核心在于构建一个能将输入映射到高维空间并保留历史信息的动态系统。本文提出一种基于循环量子特征映射的储层模型,通过重复使用固定量子电路,同时编码当前输入与来自前次输出的古典反馈信号。我们在Mackey-Glass时间序列预测任务上评估该模型,采用近期提出的CP特征映射,结果表明其均方误差低于标准经典基线(包括回声状态网络和多层感知机),同时保持紧凑的电路深度与量子比特需求。进一步分析显示,该模型具备有效记忆能力,与其预测精度一致。最后,我们研究了真实噪声的影响,发现性能对多种噪声通道具有鲁棒性,但对双量子比特门错误仍敏感,揭示了近中期实现中的关键限制。
原文摘要 · Abstract (English)
Reservoir computing promises a fast method for handling large amounts of temporal data. This hinges on constructing a good reservoir--a dynamical system capable of transforming inputs into a high-dimensional representation while remembering properties of earlier data. In this work, we introduce a reservoir based on recurrent quantum feature maps where a fixed quantum circuit is reused to encode both current inputs and a classical feedback signal derived from previous outputs. We evaluate the model on the Mackey-Glass time-series prediction task using our recently introduced CP feature map, and find that it achieves lower mean squared error than standard classical baselines, including echo state networks and multilayer perceptrons, while maintaining compact circuit depth and qubit requirements. We further analyze memory capacity and show that the model effectively retains temporal information, consistent with its forecasting accuracy. Finally, we study the impact of realistic noise and find that performance is robust to several noise channels but remains sensitive to two-qubit gate errors, identifying a key limitation for near-term implementations.
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