[论文解读] Coherent photonic crossbar as a universal linear operator

George Giamougiannis, Apostolos Tsakyridis+4 more|arXiv (Cornell University)|Aug 24, 2022

Neural Networks and Reservoir Computing被引用 10

一句话总结

本文提出了一种新型相干光子交叉bar（Xbar）架构，可普遍实现任意实数或复数线性算子，具备直接映射矩阵元素至单个节点的单步编程能力。与基于SVD的方案不同，Xbar实现插入损耗的线性扩展，支持完整保真度恢复，在损耗和相位误差容错性方面优于现有方法，整体损耗显著降低且鲁棒性更强。

ABSTRACT

Linear optics aim at realizing any real- and/or complex-valued matrix operator via optical elements, addressing a broad field of applications in the areas of quantum photonics, microwave photonics and optical neural networks. The transfer of linear operators into photonic experimental layouts typically relies on Singular Value Decomposition (SVD) techniques combining meshes of cascaded 2x2 Mach Zehnder Interferometers (MZIs), with the main challenges being the precision in the experimental representation of the targeted matrix, referred to as fidelity, and the overall insertion loss. We demonstrate a novel interferometric coherent photonic crossbar architecture (Xbar) that demarcates from state-of-the-art SVD implementations and can realize any linear operator, supporting full restoration of the loss-induced fidelity. Its novel interferometric design allows for the direct mapping of each matrix element to a single, designated Xbar node, bringing down the number of programming steps to only one. We present the theoretical foundations of the Xbar, proving that its insertion losses scale linearly with the node losses as opposed to the exponential scaling witnessed by the SVD counterparts. This leads to a matrix design with significantly lower overall insertion losses compared to SVD-based schemes when utilizing state-of-the-art silicon photonic fabrication metrics, allowing for alternative node technologies with lower energy consumption and higher operational speed credentials to be employed. Finally, we validate that our Xbar architecture is the first linear operator that supports fidelity restoration, outperforming SVD schemes in loss- and phase-error fidelity performance and forming a significantly more robust layout to loss and phase deviations.

研究动机与目标

• 开发一种光子架构，能够以高保真度普遍实现任意实值或复值线性算子。
• 克服基于SVD的光子实现方案的局限性，特别是插入损耗的指数级扩展以及对损耗和相位误差的差强人意的容错能力。
• 通过一种新型干涉设计，将每个矩阵元素直接映射至单个Xbar节点，实现矩阵元素的直接、单步编程。
• 实现插入损耗与节点损耗的线性扩展，与基于SVD的系统中指数级扩展形成鲜明对比。
• 首次实现支持在损耗和相位偏差下完整保真度恢复的光子线性算子。

提出的方法

• Xbar架构采用一种新型干涉设计，其中每个矩阵元素被直接映射至一个独立的专用Xbar节点，消除了级联MZI链路。
• 系统通过在交叉bar拓扑中利用相干光干涉，实现任意线性变换，通过在每个节点精确控制相位和振幅。
• 理论分析证明，插入损耗与单个节点损耗呈线性关系，与基于SVD的级联MZI网络中观察到的指数级扩展形成对比。
• 该设计通过直接将整个矩阵映射至单个Xbar节点，实现单步编程，相比迭代式基于SVD的校准，显著降低了复杂度和误差累积。
• 通过交叉bar结构内部的相干反馈机制，动态补偿由损耗引起的失真，实现保真度恢复。
• 理论建模结合了最先进的硅光子制造指标，以在实际条件下评估性能。

实验结果

研究问题

• RQ1 能否通过直接、非级联的节点映射，实现一种光子架构，以普遍适用的方式实现任意线性算子？
• RQ2 Xbar架构是否实现与节点损耗成线性关系的插入损耗扩展，与基于SVD系统的指数级扩展形成对比？
• RQ3 Xbar设计能否恢复因器件缺陷（如插入损耗和相位误差）导致的保真度损失？
• RQ4 在实际制造约束条件下，Xbar在保真度和鲁棒性方面与基于SVD的光子实现方案相比表现如何？
• RQ5 Xbar能否通过支持低损耗节点技术，实现更低的能耗和更高的运行速度？

主要发现

• Xbar架构实现了与节点损耗成线性关系的插入损耗扩展，这是对基于SVD的光子系统中观察到的指数级扩展的根本性改进。
• 该系统支持完整保真度恢复，使其成为首个能够从损耗引起的失真中恢复的光子线性算子。
• Xbar在损耗和相位误差下的保真度性能方面优于基于SVD的方案，表现出对器件缺陷更强的鲁棒性。
• 通过将每个矩阵元素直接映射至唯一的Xbar节点，该设计将编程复杂度降低至单步，显著减少了校准开销。
• 在最先进的硅光子制造指标下，Xbar相比基于SVD的替代方案实现了显著更低的整体插入损耗。
• 该架构为采用低能耗、高速节点技术铺平了道路，因其对损耗和相位偏差的敏感度更低。