发表机构
School of Physics and Astronomy, Shanghai Jiao Tong University; School of Integrated Circuits, Shanghai Jiao Tong University（上海交通大学物理与天文学院; 上海交通大学集成电路学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为时分复用光子量子储层提出精确的任务-风险多项式桥接，通过三步推导实现无需试错模拟的架构剪枝，并在七个数据集上验证至机器精度。
AI 中文摘要
时分复用（TDM）光子储层通常依据其在少数数据集上的得分来评判，这几乎无法反映芯片的整体性能；其设计方式是通过枚举候选电路并逐一模拟，效率低下且无法保证找到优良结构。对于带有数据调制门或光源及岭回归读出器的时展开无源线性网络，我们通过三步推导出从任务到预测风险的精确桥接。（i）任务特征：有限次实验的风险仅依赖于时间序列通过其训练窗口的有限统计量及其与目标的关联，这些统计量由编码和光路选择。（ii）编码：每个输出矩是关于数据调制位点特征的多项式，其次数和支撑集由光路元组界定。门编码读取特征函数并创建跨时滞的相互作用；压缩编码读取矩生成函数，位移编码读取低阶矩，且对于正交接收器，它们分别仅产生加性模型和线性模型，适用于任何拓扑。（iii）读出：对于零差、外差和光子数接收器，风险精确闭合，其对实验次数的依赖是对信噪比模式的显式求和；阈值点击允许具有认证误差的有限字典近似。网络中不共享光的各部分携带独立状态，接收器仅通过连接它们的测量事件来组合这些状态。对七个数据集的检查确认了所有精确陈述至机器精度。因此，这三步产生了一个有用的候选TDM架构空间，通过精确陈述而非试错模拟进行剪枝，未来可指导针对目标需求选择TDM芯片。
英文摘要
Time-multiplexed (TDM) photonic reservoirs are usually judged by their scores on a few datasets, which say little about a chip's overall performance, and designed by enumerating candidate circuits and simulating each one, which is inefficient and gives no guarantee of finding a good structure. For a time-unrolled passive linear network with data-modulated gates or sources and a ridge readout, we derive an exact bridge from the task to the prediction risk in three steps. (i) Task features: the finite-shot risk depends on the time series only through finitely many statistics of its training windows and their correlations with the target, selected by the encoding and the optical paths. (ii) Encoding: every output moment is a polynomial in the features of the data-modulated sites, with degree and support bounded by tuples of optical paths. Gate encoding reads the characteristic function and creates interactions across time lags; squeezing encoding reads the moment-generating function and displacement encoding low-order moments, and with quadrature receivers they yield only additive and linear models, respectively, for every topology. (iii) Readout: for homodyne, heterodyne and photon-number receivers the risk closes exactly, and its dependence on the number of shots is an explicit sum over signal-to-noise modes; threshold clicks admit finite-dictionary approximations with certified error. Parts of the network that share no light carry independent states, which a receiver combines only through measurement events that join them. Checks on seven datasets confirm every exact statement to machine precision. The three steps thus yield a useful space of candidate TDM architectures, pruned by exact statements rather than by trial simulation, which can in future guide the selection of TDM chips for target requirements.
Comments33 pages, 7 figures, 14 tables
