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arXiv:2408.00669 · Physical Review Research

Low-depth two-unitary design of programmable photonic circuits

Suren A. Fldzhyan, M. Yu. Saygin, Stanislav S. Straupe

Published Nov 25, 2024• 7 citations
arXivHTMLPDF

Abstract

Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce what we believe to be a novel architecture of photonic circuits capable of implementing non-unitary transfer matrices, usually required by photonic neural networks, iterative equation solvers, or quantum samplers. Our architecture exploits compact low-depth beam-splitter meshes rather than bulky fully connected mixing blocks used in previous designs, making it more compatible with planar integrated photonics technology. We have shown that photonic circuits designed with our architecture have lower depth than their standard counterparts and are extremely tolerant of hardware errors.

DOI
10.1103/9fg1-fdfl

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APL Photonics•Feb 1, 2025•6 citations
Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce what we believe to be a novel architecture of photonic circuits capable of implementing non-unitary transfer matrices, usually required by photonic neural networks, iterative equation solvers, or quantum samplers. Our architecture exploits compact low-depth beam-splitter meshes rather than bulky fully connected mixing blocks used in previous designs, making it more compatible with planar integrated photonics technology. We have shown that photonic circuits designed with our architecture have lower depth than their standard counterparts and are extremely tolerant of hardware errors.
Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. Identified reference point allows for the subtraction to be carried out electronically after detection, avoiding the interferometric subtraction loss. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach-Zehnder interferometers, these systems have demonstrated significant potential in microwave photonics applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach-Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3x3 and 4x4 random unitary matrices yields fidelities > 98% and bit precisions over 5 bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.
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.
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+1N+1N+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.
General-purpose programmable photonic processors offer a flexible foundation for integrating various functionalities within a single chip. A two-dimensional hexagonal waveguide mesh of Mach Zehnder interferometers has been shown to have great potential in the field of microwave photonics. Additionally, they are a promising platform for the creation of unitary linear transformations, which are key elements in photonic neural networks, In this article, we expand the portfolio of available applications for recirculating bricks mesh architecture to quantum technologies. We will show that a single programmable optical system is capable of performing various functions depending on the requirements. In particular, we will focus in this work on boson sampling, a task that best demonstrates quantum advantage, as well as on tasks that enable the determination of photon indistinguishability, which plays a key role in photonic quantum technologies. We will also show that, in addition to spatial modes, the same optical system can be equally well-suited for work on temporal modes through the implementation of an appropriate number of loops.
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach–Zehnder interferometers, these systems have demonstrated significant potential in microwave photonic applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach–Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3 × 3 and 4 × 4 random unitary matrices yields fidelities >98% and bit precisions over five bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.