In universal linear optics, programmable photonic circuits perform an arbitrary linear transformation by the sequential multiplication of two-level achromatic unitary operators. Based on cascaded optical resonator-based building blocks, we construct an arbitrary multi-wavelength unitary operator.
Programmable photonic integrated circuits have mainly been developed based on the single wavelength channel operation of fundamental building blocks consisting of Mach-Zehnder interferometers (MZIs) with tunable phase shifters. We propose and study optical circuit models consisting of cascaded optical resonators that enable the independent operation of multiple wavelength channels in a more compact footprint than the conventional MZIs. By adopting experimental values reported for silicon micro-ring resonators, the fidelities of different types of 2×2 unitary transformations and higher-dimensional unitary transformations are examined by employing the Reck algorithm and the Clements algorithm.
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 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.
Universal multiport interferometers based on Mach–Zehnder meshes are becoming a core building block for photonic neural-network accelerators and photonic quantum processors. This thesis presents the design, calibration, and control of such a programmable photonic integrated circuit (PIC). A fully automated software and hardware platform is developed to characterize and control the tunable elements of the PIC, enabling robust implementation of arbitrary linear optical transformations as well as target unitary operations. Using the calibrated device model, the control framework programs the PIC to realize specific unitaries and evaluates their performance through fidelity metrics computed from measured transfer matrices. By covering the complete stack from chip design to automated calibration and high-level unitary programming, this work establishes a scalable framework for design and operation of programmable photonic processors.