Optical computing is emerging as a promising platform for energy-efficient, high-throughput hardware in deep learning. A key challenge lies in the realization of optical matrix–vector multiplication, which often requires O ( N 2 ) modulators for the exact synthesis of N × N matrices, limiting its scalability. In this study, we propose an approximate matrix realization method using multi-plane light conversion (MPLC) that reduces both the system size and the number of phase shifters while maintaining acceptable error bounds. This approach introduces low-entropy mode mixers, in which couplings between optical modes are weak. We demonstrate that such mixers can preserve computational accuracy while reducing hardware requirements, enabling more flexible and compact implementations in unitary converters using MPLC. We further investigate converters with fewer phase-shifter layers than the theoretical minimum and show that they function as approximate converters by tolerating predefined error thresholds, achieving sub-quadratic scaling. To identify efficient architectures for implementing general linear matrices using unitary converters, we compare block-encoding (BE) and singular-value decomposition (SVD) schemes. Results indicate that BE exhibits superior iterative configuration properties. By characterizing the trade-offs between entropy of mode mixers, number of phase shifters, and error tolerance, this study provides a framework for designing scalable and efficient approximate optical converters. Finally, using model quantization techniques, we demonstrate that the proposed method reduces the number of required phase shifters by half while preserving the accuracy of a text classification model, highlighting the effectiveness of error-tolerant model training for analog computing platforms.
Optical computing is emerging as a promising platform for energy-efficient, high-throughput hardware in deep learning. A key challenge lies in the realization of optical matrix–vector multiplication, which often requires O ( N 2 ) modulators for the exact synthesis of N × N matrices, limiting its scalability. In this study, we propose an approximate matrix realization method using multi-plane light conversion (MPLC) that reduces both the system size and the number of phase shifters while maintaining acceptable error bounds. This approach introduces low-entropy mode mixers, in which couplings between optical modes are weak. We demonstrate that such mixers can preserve computational accuracy while reducing hardware requirements, enabling more flexible and compact implementations in unitary converters using MPLC. We further investigate converters with fewer phase-shifter layers than the theoretical minimum and show that they function as approximate converters by tolerating predefined error thresholds, achieving sub-quadratic scaling. To identify efficient architectures for implementing general linear matrices using unitary converters, we compare block-encoding (BE) and singular-value decomposition (SVD) schemes. Results indicate that BE exhibits superior iterative configuration properties. By characterizing the trade-offs between entropy of mode mixers, number of phase shifters, and error tolerance, this study provides a framework for designing scalable and efficient approximate optical converters. Finally, using model quantization techniques, we demonstrate that the proposed method reduces the number of required phase shifters by half while preserving the accuracy of a text classification model, highlighting the effectiveness of error-tolerant model training for analog computing platforms.
The integrated universal linear optical processor realized via multi-plane light conversion (MPLC) features low hardware complexity and high fabrication robustness, suitable for diverse photonic processing tasks. However, the lack of validated calibration protocols limits its universality and potential. Here, we propose a machine-learning-based calibration method and verify it using an eight-mode silicon photonic processor composed of interleaved multiport directional couplers and phase-shifter arrays. We characterize coupler transfer matrices and current-phase responses of individual phase shifters. To validate the robustness, we demonstrate its universality with Haar-random unitary matrices at wavelengths of 1500, 1550, and 1580 nm, and under partial phase-shifter deactivation. With this white-boxed device, we also demonstrate high-dimensional quantum gates and quantum reservoir computing for handwritten digit classification. Our work advances integrated MPLC-based universal linear optics and paves the way for large-scale, fabrication-robust, broadband hardware for classical and quantum photonic information processing.
Programmable linear optical interferometers are a core primitive in optical signal processing, quantum information processing, and photonic computing. Existing photonic-integrated implementations realize arbitrary M-mode unitaries using Mach--Zehnder-interferometer meshes whose footprint and accumulated loss scale with O(M2) optical components. Here we analyze and experimentally demonstrate a programmable architecture for implementing linear optical transformations directly on spatially tiled free-space {\em pixel modes} using multi-plane light conversion (MPLC). In this architecture, M spatial modes arranged on a transverse lattice undergo a unitary transformation and are mapped to M output modes of identical geometry through a sequence of programmable phase masks separated by free-space propagation segments. Numerical simulations show that arbitrary M-mode unitaries can be compiled to a desired high fidelity using a number of phase planes that scales approximately linearly with M. Using a spatial-light-modulator-based MPLC, we experimentally demonstrate programmable interferometers acting on up to 16 spatial pixel modes, including tunable beamsplitters, Hadamard unitaries, spatial permutations, and partial unitaries on select subsets of modes. These results establish MPLC-based pixel-mode interferometers as a promising architecture for programmable linear optics with applications in classical and quantum optical interconnects, photonic switching, and quantum information processing.
Programmable unitary photonic devices are emerging as promising tools to implement unitary transformation for quantum information processing, machine learning, and optical communication. These devices typically use a rectangular mesh of Mach-Zehnder interferometers, which has a clear mathematical structure and can be configured deterministically. However, this mesh architecture is sensitive to fabrication errors, and the correction techniques are still under investigation. In contrast, the multiplane light-conversion (MPLC) architecture is more robust against fabrication errors, but a deterministic method for configuring the converter has not yet been developed due to its complex mathematical structure. In this work, we propose a fast iterative configuration method for MPLC, following the mathematical review of the matrix distance and proposal of an alternative norm. We show through numerical simulations that adding a few redundant layers significantly improves the convergence of the MPLC architecture, making it a practical and attractive option. We also consider the effects of finite resolution and cross-talk in phase shifters in our simulations. In addition, we propose a phase-insensitive distance suited for applications using only intensity detections. Our method demonstrates orders of magnitude better accuracy and a 20-fold speedup compared to previous approaches.
In recent years, there has been growing interest in analog information processing and unconventional computing using Photonic Integrated Circuits (PICs) to address the increasing demands of next-generation computing. This has driven the development of on-chip architectures capable of implementing fundamental linear operations such as matrix-vector multiplication (MVM), which plays a central role in fields such as quantum information processing and the acceleration of deep neural networks. Within the feed-forward paradigm, interleaved meshes of Mach–Zehnder Interferometers (MZIs) have emerged as the leading architecture for programmable integrated photonics (PIP), enabling real-time implementation of arbitrary linear transformations using tunable phase shifter elements. More recently, an alternative class of programmable photonic architectures based on Multi-Plane Light Conversion (MPLC) has been proposed, consisting of alternating diagonal phase-shifter layers and multimode mixing elements. Although these architectures lack a deterministic synthesis algorithm for the phase actuators, they have been shown to offer several advantages over conventional MZI-based architectures. In this thesis we investigate the properties and universal capabilities of MPLC architectures utilizing unequally spaced coupled waveguide arrays (CWAs), with a particular emphasis on the well-known Jx-lattice. Defect tolerance and self-calibration properties are studied, demonstrating substantially greater robustness to imperfections than conventional MZI meshes. We further introduce several extensions of the MPLC architecture that demonstrate its flexibility, such as the redistribution of amplitude modulators and their interchangeable use with phase shifters to realize universal transformations with a near-minimal number of tunable units. Collectively, these results provide a broader understanding of the capabilities of MPLC architectures and establish a foundation for their application as a flexible alternative and complement to MZI-based designs.
Light with complex structures in polarization, phase and amplitude, has attracted a lot of attention in a broad range of applications and fundamental studies in classical and quantum optics. Along with the increased interest in structured light comes a need for efficient modulation platforms operating simultaneously for many modes. Multi plane light conversions (MPLC), i.e., multiple consecutive phase modulations in combination with free space propagation, have enabled such unitary transformations, which are usually built by bulky optical components, limited to scalar modulation, or rely on advanced nanofabrication techniques. Here, we demonstrate an efficient, monolithic MPLC architecture through direct laser writing in standard fused silica glass, resulting in a device with a compact form factor of only a few cubic millimeters. Our scheme is based on volumetric engineering of the glass's birefringence through laser-written nanogratings, which enables spatial control over full vectorial light structures. To showcase the approach's potential for integrated multimode-multipath optical networks, we demonstrate multi-mode unitary transformations, mode conversions, and complex beam-splitting for scalar light. We further extend the MPLC operation to vectorial light and implement various polarization-controlled spatial mode operations as well as the transformation of the topology of an optical Skyrmion. Finally, we highlight our scheme's promise for optical communications and implement a miniaturized multiplexer for spatial modes and polarization operating at telecom wavelength.
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.