研究量子系统中混乱与噪声对时间信息处理的影响。
Role of scrambling and noise in temporal information processing with quantum systems
- 用高阶酉设计模拟混沌量子储层，分析其可扩展性与记忆保持能力。
- 无噪声下测量读出随储层规模指数集中，但输入记忆随迭代与规模指数衰减。
- 在局部噪声下，早期输入记忆随时间指数衰减，适合关注量子计算稳定性的研究者。
混沌量子系统因其在时间信息处理中的有效性而受到关注。本文研究了一种量子储层处理框架，涵盖多种基于量子系统的物理计算模型。通过高阶酉设计建模混沌储层，在无噪声与有噪声两种情形下分析了模型的可扩展性与记忆保留能力。在无噪声条件下，测量读出随储层规模增大呈指数集中，且不随储层迭代次数增加而恶化；然而，若仅重复使用小型混沌储层处理大规模问题，则除非承担指数级采样开销，否则泛化性能会下降。同时，早期输入和初始状态的记忆均随储层规模与迭代次数呈指数衰减。在有噪声情形下，我们证明对于局域噪声通道，记忆也随时间呈指数衰减。这些结果推动了新的证明技术发展，用于界定时间量子模型中的浓度边界。
原文摘要 · Abstract (English)
Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models.
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