利用分布式架构学习量子态函数
Learning functions of quantum states with distributed architectures
AI总结：
本文提出分布式架构用于学习量子态函数，通过减少资源消耗实现高效量子属性学习。
摘要：
分布式架构在量子机器学习中日益受到关注，作为克服硬件限制和实现可扩展量子信息处理的手段。在此背景下，我们分析了分布式量子极限学习机（QELM）架构的设计与性能，旨在直接从数据中学习量子态函数，限制测量为易于实现的计算基投影测量。目标是确定哪些方案能够有效恢复输入量子态的特定属性，包括线性和非线性特征，同时量化资源需求，即测量和存储器维度。我们比较了标准三层QELM与由多个独立三层单元组成的空乘复用架构，对于线性（量子）任务，显示了每单位资源需求的线性减少。对于非线性特性，研究考察了多注射架构，并引入了一种新的分布式设计，该设计在空乘复用框架内引入子系统间的纠缠，通过重构多项式目标、雷尼熵和纠缠度量等复杂非线性量来评估其性能。我们的结果表明，分布式设计通过增加相互作用子系统的数量并减少资源消耗，能够重构更高阶的非线性特性，而不是增加单个存储器的规模，从而提供了一条可扩展且硬件高效的量子属性学习途径。
英文摘要：
Distributed architectures are gaining prominence in quantum machine learning as a means to overcome hardware limitations and enable scalable quantum information processing. In this context, we analyze the design and performance of distributed Quantum Extreme Learning Machine (QELM) architectures for learning functions of quantum states directly from data, restricting measurements to easily implementable projective measurements in the computational basis. The aim is to determine which schemes can effectively recover specific properties of input quantum states, including both linear and nonlinear features, while also quantifying the resource requirements in terms of measurements and reservoir dimensionality. We compare standard three-layer QELM with a spatially multiplexed architecture composed of multiple independent three-layer units for linear (quantum) tasks, showing a linear reduction in resource requirements per unit. For nonlinear properties, the study examines the multiple-injection architecture and introduces a novel distributed design that incorporates entanglement between subsystems within a spatially multiplexed framework, evaluating its performance through the reconstruction of complex nonlinear quantities such as polynomial targets, Rényi entropy, and entanglement measures. Our results demonstrate that the distributed design enables the reconstruction of higher-order nonlinearities by increasing the number of interacting subsystems with reduced resources, rather than increasing the size of an individual reservoir, providing a scalable and hardware-efficient route to quantum property learning.
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