Abstract A design framework to implement non-unitary input–output operations to a practical unitary photonic integrated circuit is described. This is achieved by utilising the cosine-sine decomposition to recover the unitarity of the original operation. The recovered unitary operation is decomposed into fundamental unitary building blocks, forming a photonic integrated circuit network based on directional couplers and waveguide phase shifters. The individual building blocks are designed and optimised by three-dimensional full-wave simulations and scaled up using a circuit approach. The paper investigates the scalability and robustness of the design approach. Our study demonstrates that the proposed approach of performing unitary matrix completion can be applied to any arbitrary matrices. This design approach allows for implementation of non-unitary operations to perform various linear functions in neuromorphic photonics for computing, sensing, signal processing and communications.
Abstract A design framework to implement non-unitary input–output operations to a practical unitary photonic integrated circuit is described. This is achieved by utilising the cosine-sine decomposition to recover the unitarity of the original operation. The recovered unitary operation is decomposed into fundamental unitary building blocks, forming a photonic integrated circuit network based on directional couplers and waveguide phase shifters. The individual building blocks are designed and optimised by three-dimensional full-wave simulations and scaled up using a circuit approach. The paper investigates the scalability and robustness of the design approach. Our study demonstrates that the proposed approach of performing unitary matrix completion can be applied to any arbitrary matrices. This design approach allows for implementation of non-unitary operations to perform various linear functions in neuromorphic photonics for computing, sensing, signal processing and communications.
ABSTRACT Unitary operations lie at the heart of quantum computing, enabling the manipulation of quantum states in a reversible and coherent manner. In photonic integrated circuits, these operations are realized using photonic waveguide architectures composed of passive beam splitters and reconfigurable phase shifters. This review provides an overview of photonic circuit architectures designed to implement unitary transformations. We examine various design strategies, material platforms, and the current state‐of‐the‐art in realizing high‐fidelity photonic unitaries. In addition, we explore the theoretical underpinnings of photon transport in such circuits, shedding light on the quantum behavior of light in unitary photonic systems. Finally, we introduce a simulation framework for modeling and analyzing these photonic networks, offering a practical tool for research and development in this rapidly growing field.
Abstract Programmable photonic integrated circuits represent an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Programmable photonics provides a flexible platform that can be reconfigured to perform multiple tasks, thereby holding great promise for revolutionizing future optical networks and quantum computing systems. Over the past decade, there has been constant progress in developing several different architectures for realizing programmable photonic circuits that allow for realizing arbitrary discrete unitary operations with light. Here, we systematically investigate a general family of photonic circuits for realizing arbitrary unitaries based on a simple architecture that interlaces a fixed intervening layer with programmable phase shifter layers. We introduce a criterion for the intervening operator that guarantees the universality of this architecture for representing arbitrary N×N N × N unitary operators with N+1 N + 1 phase layers. We explore this criterion for different photonic components, including photonic waveguide lattices and meshes of directional couplers, which allows the identification of several families of photonic components that can serve as the intervening layers in the interlacing architecture. Our findings pave the way for efficiently designing and realizing novel families of programmable photonic integrated circuits for multipurpose analog information processing.
Programmable photonic integrated circuits are an emerging technology that amalgamates photonics and electronics, paving the way for light-based information processing at high speeds and low power consumption. Considering its wide range of applications as one of the most fundamental mathematical operations, there has been considerable interest in developing reliably implementable programmable circuit architectures that perform matrix-vector multiplication. Recently, it was shown that discrete unitary operations can be parameterized by interlacing fixed operators with diagonal phase parameters realized with phase shifter arrays. We show that these decompositions are a special case of a broader class of factorizations that enable parametrization of arbitrary complex matrices. The proposed representation of an $N\ifmmode\times\else\texttimes\fi{}N$ matrix is given by N+1 amplitude-and-phase-modulation layers interlaced with a fixed unitary layer that can be implemented, for example, via a coupled waveguide array. Thus, we introduce an architecture for physically implementing discrete linear operations, enabling the development of novel families of programmable photonic circuits for on-chip analog information processing.
Abstract Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization of classical and quantum information processing. The ability of implementing any n‐dimensional unitary signal transformation by using a reconfigurable optical hardware has recently led to the pioneering concept of programmable linear optical processor, whose basic building block (BB) must be correctly designed to guarantee that the whole system is able to perform universal (i.e., arbitrary) unitary matrix transformations. Here, it is demonstrated that the present architectures of the BB do not fulfil the universal unitary property (at least) in optical processors, limiting the number of unitary matrix transformations that may be generated. Aiming to solve this fundamental constraint, the theoretical tools required to analyze and design universal unitary optical circuits and their corresponding BBs are presented. The consequences of this mathematical framework are explored, obtaining a simple route to implement different BB architectures, all of them guaranteeing a true universal unitary functionality in the resulting optical processors. These findings may pave the way to revisit the design of high‐dimensional unitary optical processors, unleashing the potential of programmable integrated photonics technology.
Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization of classical and quantum information processing. The ability of implementing any n-dimensional unitary signal transformation by using a reconfigurable optical hardware has recently led to the pioneering concept of programmable linear optical processor, whose basic building block (BB) must be correctly designed to guarantee that the whole system is able to perform n × n universal (i.e., arbitrary) unitary matrix transformations. Here, it is demonstrated that the present architectures of the BB do not fulfil the universal unitary property (at least) in 2 × 2 optical processors, limiting the number of unitary matrix transformations that may be generated. Aiming to solve this fundamental constraint, the theoretical tools required to analyze and design 2 × 2 universal unitary optical circuits and their corresponding BBs are presented. The consequences of this mathematical framework are explored, obtaining a simple route to implement different BB architectures, all of them guaranteeing a true universal unitary functionality in the resulting 2 × 2 optical processors. These findings may pave the way to revisit the design of high-dimensional unitary optical processors, unleashing the potential of programmable integrated photonics technology.
Abstract Implementing arbitrary unitary transformations is crucial for applications in quantum computing, signal processing, and machine learning. Unitaries govern quantum state evolution, enabling reversible transformations critical in quantum tasks like cryptography and simulation and playing key roles in classical domains such as dimensionality reduction and signal compression. Integrated optical waveguide arrays have emerged as a promising platform for these transformations, offering scalability for both quantum and classical systems. However, scalable and efficient methods for implementing arbitrary unitaries remain challenging. Here, we present a theoretical framework for realizing arbitrary unitary matrices through programmable waveguide arrays (PWAs). We provide a mathematical proof demonstrating that cascaded PWAs can implement any unitary matrix within practical constraints, along with a numerical optimization method for customized PWA designs. Our results establish PWAs as a universal and scalable architecture for quantum photonic computing, effectively bridging quantum and classical applications, and positioning PWAs as an enabling technology for advancements in quantum simulation, machine learning, secure communication, and signal processing.