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arXiv:2208.12033 · Journal of Lightwave Technology

A Coherent Photonic Crossbar for Scalable Universal Linear Optics

George Giamougiannis, Apostolos Tsakyridis, Yangjin Ma, Angelina R. Totovic, Miltiadis Moralis‐Pegios, David Lazovsky, Nikos Pleros

Published Jan 6, 2023• 60 citations

Abstract

We demonstrate a novel interferometric coherent photonic crossbar architecture (Xbar) that can realize any tensor operator and allows for total loss-induced fidelity restoration, offering at the same time significant dimension scalability credentials compared to respective state-of-the-art solutions. The proposed Xbar layout demarcates from the prevalent photonic schemes that rely on the implementation of intended matrices factorized via the Singular Value Decomposition (SVD); instead, it harnesses the power of interference within a novel design where each matrix element can be mapped by one-to-one correspondence to a single, designated Xbar node, bringing down the number of programming steps to only one. In this paper, we present the theoretical foundations of the Xbar, proving that its insertion losses do not scale with the node losses as opposed to the exponential scaling witnessed by the SVD based counterparts. This leads to a matrix design with significantly lower overall insertion losses and improved scalability potential compared to SVD-based schemes, allowing for the employment of alternative node technologies with lower energy consumption and higher operational speed credentials. Finally, we theoretically validate that the proposed Xbar architecture is the first linear operator that supports fidelity restoration, outperforming SVD schemes in loss- and phase-error fidelity performance.

DOI: 10.1109/jlt.2023.3234689

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We demonstrate a novel interferometric coherent photonic crossbar architecture (Xbar) that can realize any tensor operator and allows for total loss-induced fidelity restoration, offering at the same time significant dimension scalability credentials compared to respective state-of-the-art solutions. The proposed Xbar layout demarcates from the prevalent photonic schemes that rely on the implementation of intended matrices factorized via the Singular Value Decomposition (SVD); instead, it harnesses the power of interference within a novel design where each matrix element can be mapped by one-to-one correspondence to a single, designated Xbar node, bringing down the number of programming steps to only one. In this paper, we present the theoretical foundations of the Xbar, proving that its insertion losses do not scale with the node losses as opposed to the exponential scaling witnessed by the SVD based counterparts. This leads to a matrix design with significantly lower overall insertion losses and improved scalability potential compared to SVD-based schemes, allowing for the employment of alternative node technologies with lower energy consumption and higher operational speed credentials. Finally, we theoretically validate that the proposed Xbar architecture is the first linear operator that supports fidelity restoration, outperforming SVD schemes in loss- and phase-error fidelity performance.

Recently there has been growing interest in using photonics to perform the linear algebra operations of neuromorphic and quantum computing applications, aiming at harnessing silicon photonics' (SiPho) high-speed and energy-efficiency credentials. Accurately mapping, however, a matrix into optics remains challenging, since state-of-the-art optical architectures are sensitive to fabrication imperfections. This leads to reduced fidelity that degrades as the insertion losses of the optical matrix nodes or the matrix dimensions increase. In this work, we present the experimental deployment of a 4 × 4 coherent crossbar (Xbar) as a silicon chip and validate experimentally its theoretically predicted fidelity restoration credentials. We demonstrate the experimental implementation of 10,000 arbitrary linear transformations achieving a record-high fidelity of 99.997% ± 0.002, limited mainly by the measurement equipment. Our work represents an integrated optical circuit providing almost unity and loss-independent fidelity in the realization of arbitrary matrices, highlighting light's credentials in resolving complex computations.

Universal multiport interferometers that can be programmed to perform any unitary or linear transformation turn into an important building block for both classical and quantum photonics. These interferometers typically utilize the mathematical framework of U(2) unitary matrix decomposition techniques and comprise a mesh of 2 × 2 beam splitters and phase shifters. All of them are, however, inherently fidelity limited as their U(2)‐based deployment approach leads to imbalanced path losses without supporting any fidelity restoration mechanism. Herein, a novel Universal Generalized Mach–Zehnder Interferometer (UGMZI) architecture is presented that migrates from U(2) decomposition techniques and adopts a recursive U(N) decomposition, exploiting cascaded size‐augmenting N N beam splitters and phase shifters. The design can natively support fidelity restoration and safeguard absolute fidelity, while outperforming the state‐of‐the‐art designs also with respect to phase‐error‐induced fidelity performance properties. Finally, it is demonstrated that its fidelity restoration properties turn the design into the optimal architecture for constructing any real/complex‐valued matrix via the singular value decomposition (SVD) scheme.

Reconfigurable linear optical networks based on Mach-Zehnder interferometer (MZI) offer significant potential in optical information processing, particularly in emerging photonic quantum computing systems. However, device losses and calibration errors accumulate as network complexity grows, posing challenges in performing precise mapping of matrix operations. Existing architectures, such as Diamond and Bokun, introduce MZI redundancy into Reck and Clements architectures to improve reliability, which increases complexity and differential path losses that limit scalability. We propose a compact topology architecture that achieves 100% fidelity by employing a symmetrical MZI to decouple optical loss from power ratio and introducing extra MZIs to enforce uniform loss distributions. This multi-level optimization enables direct monitoring pathways while supporting precise calibration, and it approaches theoretical fidelity in practical deployments with direct implications for scalable and fault-tolerant photonic computing systems.