量子储备池计算中的费舍尔正交记忆
Fisher-Orthogonal Memory in Quantum Reservoir Computing
AI总结：
本研究将量子储备池计算的性能限制转化为局部多参数估计问题，提出费舍尔正交记忆设计原则，构造基于Clifford路由轨道等的多量子比特储备池，大幅提升延迟重构与乘积延迟任务的性能。
AI中文摘要：
量子储备池计算通过受驱多体动力学处理时间信息，但其性能最终受限于从有限测量中提取过去输入的精度。本文将这一限制表述为局部多参数估计问题，引入延迟空间量子费舍尔信息矩阵量化记忆迹的可区分性，由此确定费舍尔正交记忆为一种测量高效的设计原则：不同延迟应沿统计独立方向扰动储备池状态。我们首先利用Gill--Massar界分析单量子比特极限，揭示最优写入-存储-路由权衡；基于该结构，我们构造基于Clifford路由轨道和Singer循环泡利代数的可解多量子比特储备池，其动力学产生具有可控耗散轮廓的对角、可解析编程的费舍尔记忆矩阵。在有限次采样的局部泡利读出下，这些储备池保留清晰的记忆窗口，在线性延迟重构和非线性乘积延迟任务中均显著优于优化后的随机伊辛储备池；非线性优势源于继承相同泡利路由结构的二阶响应通道。我们的结果为实现测量高效的量子储备池计算提供了可解析控制的途径。
英文摘要：
Quantum reservoir computing processes temporal information through driven many-body dynamics, but its performance is ultimately limited by how accurately past inputs can be extracted from finite measurements. Here we formulate this limitation as a local multiparameter estimation problem and introduce a delay-space quantum Fisher information matrix to quantify the distinguishability of information stored at different delays. This perspective identifies Fisher-orthogonal memory as a measurement-efficient design principle: different delays should perturb the reservoir state along mutually Fisher-orthogonal directions. We first analyze the single-qubit limit using the Gill--Massar bound, revealing an optimal write-store-routing trade-off. Guided by this structure, we construct solvable multi-qubit reservoirs based on Clifford routing orbits and Singer-cycle Pauli algebra. The resulting dynamics yield diagonal delay-space QFIMs with analytically programmable fading profiles. Under finite-shot local Pauli readout, these reservoirs retain sharp memory windows that are absent in a validation-selected Ising baseline. Their product-task behavior is governed by second-order responses inherited from the same Pauli-routing algebra. Our results provide an analytically controlled route toward measurement-efficient quantum reservoir computing.
