A Coherent Photonic Crossbar for Scalable Universal Linear Optics

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.