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arXiv:2505.24032

Leveraging machine learning features for linear optical interferometer control

Sergei S. Kuzmin, I. V. Dyakonov, Stanislav S. Straupe

Published May 29, 2025• 0 citations
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Abstract

We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on either an analytical method for deriving the unitary matrix from a set of phase shifts or an optimization routine when such decomposition is not available. Our algorithm employs a supervised learning approach, aligning the interferometer model with a training set derived from the device being studied. A straightforward optimization procedure leverages this trained model to determine the phase shifts of the interferometer with a specific architecture, obtaining the required unitary transformation. This approach enables the effective tuning of interferometers without requiring a precise analytical solution, paving the way for the exploration of new interferometric circuit architectures.

DOI
10.48550/arxiv.2505.24032

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We have developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on either an analytical method for deriving the unitary matrix from a set of phase shifts or an optimization routine when such decomposition is not available. Our algorithm employs a supervised learning approach, aligning the interferometer model with a training set derived from the device being studied. A straightforward optimization procedure leverages this trained model to determine the phase shifts of the interferometer with a specific architecture, obtaining the required unitary transformation. This approach enables the effective tuning of interferometers without requiring a precise analytical solution, paving the way for the exploration of new interferometric circuit architectures.
We developed an algorithm that constructs a model of a reconfigurable optical interferometer, independent of specific architectural constraints. The programming of unitary transformations on the interferometer's optical modes relies on either an analytical method for deriving the unitary matrix from a set of phase shifts or an optimization routine when such decomposition is not available. Our algorithm employs a supervised learning approach, aligning the interferometer model with a training set derived from the device being studied. A straightforward optimization procedure leverages this trained model to determine the phase shifts of the interferometer with a specific architecture, obtaining the required unitary transformation. This approach enables the effective tuning of interferometers without requiring a precise analytical solution, paving the way for the exploration of new interferometric circuit architectures.
Integrated photonic technologies have recently shown significant advances, enabling the possibility to implement reconfigurable interferometers with increasing size. One of the main tasks to fully exploit the capabilities of reconfigurable integrated interferometers is the possibility to precisely program their operation to perform a desired target unitary. While recipes are known for circuit layouts based on a cascade of beam-splitter and phase-shifter operations, a methodology applicable for reconfigurable continuously-coupled waveguide arrays is currently missing. Here, we devise a machine learning based approach for this task, using a black box methodology that does not rely on precise a-priori modeling of the circuit internal architectures. We verify the effectiveness and the robustness of this approach via numerical simulations on different continuously-coupled waveguides layouts, either with planar or 3D structures. The proposed method makes use of a limited number of single- and two-photon measurements, making it suitable for optical quantum information processing. The obtained results open the perspective of employing this methodology as an effective tool to program the operation of integrated interferometers designed via different architectures.
We develop the learning algorithm to build an architecture agnostic model of a reconfigurable optical interferometer. A procedure of programming a unitary transformation of optical modes of an interferometer either follows an analytical expression yielding a unitary matrix given a set of phase shifts or requires an optimization routine if an analytic decomposition does not exist. Our algorithm adopts a supervised learning strategy which matches a model of an interferometer to a training set populated by samples produced by a device under study. A simple optimization routine uses the trained model to output phase shifts corresponding to a desired unitary transformation of the interferometer with a given architecture. Our result provides the recipe for efficient tuning of interferometers even without rigorous analytical description which opens opportunity to explore new architectures of the interferometric circuits.
Reconfigurable photonics have rapidly become an invaluable tool for information processing. Light-based computing accelerators are promising for boosting neural network learning and inference and optical interconnects are foreseen as a solution to the information transfer bottleneck in high-performance computing. In this study, we demonstrate the successful programming of a transformation implemented using a reconfigurable photonic circuit with a non-conventional architecture. The core of most photonic processors is an MZI-based architecture that establishes an analytical connection between the controllable parameters and circuit transformation. However, several architectures that are substantially more difficult to program have improved robustness to fabrication defects. We use two algorithms that rely on different initial datasets to reconstruct the circuit model of a complex interferometer, and then program the required unitary transformation. Both methods performed accurate circuit programming with an average fidelity greater than 99% and 97%, respectively. Our results provide a strong foundation for the introduction of non-conventional interferometric architectures for photonic information processing.
Abstract Tunable linear-optical interferometers are a key element in the implementation of both classical and quantum information technologies. At the same time, during the production process, these systems are subject to various instrumental imperfections and it is necessary to be able to determine with what accuracy and what transformations the manufactured device is capable to reproduce. For integrated devices, such tasks are difficult to perform due to the difficulties in obtaining direct access to individual optical elements of the circuit. Existing methods for reconstructing the transfer matrix of tunable linear-optical interferometers require measuring the phases of its matrix elements at different values of control signals in the circuit, which is also an experimentally time-consuming task. However, in some cases, it is possible to construct a mathematical model of the circuit that works for any values of its control signals, measuring only partial amplitude transmission coefficients at the outputs of the circuit, which significantly simplifies reconstruction and is relevant in a number of applications. In this paper, we performed numerical and experimental approbation of the method on the example of a linear-optical interferometer with four inputs and four outputs with a universal architecture based on mixing layers. The average fidelity value of the reconstruction of the reduced transfer matrix of the optical interferometer, taking into account realistic noise in the experiment, was 99.9% and can be improved due to the proven stability of the model to them.
We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an N×NN \times NN×N unitary matrix into interlaced discrete fractional Fourier transforms and NNN-parameter diagonal phase shifts. We show that such a configuration can represent arbitrary unitary operators with N+1N+1N+1 phase layers. We discuss a gradient-based algorithm for finding the optimal phase parameters for implementing a given unitary matrix. By increasing the number of phase layers beyond the critical value of N+1N+1N+1, the optimization consistently converges faster as the system becomes over-determined. We propose an integrated photonic circuit realization of this architecture with coupled waveguide arrays and reconfigurable phase modulators. The proposed architecture can pave the way for developing novel families of programmable photonic circuits for optical classical and quantum information processing.