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arXiv:2307.03635 · Optics Express

Fast reconstruction of programmable integrated interferometers

B. I. Bantysh, Konstantin G. Katamadze, Andrey Yu. Chernyavskiy, Yu. I. Bogdanov

Published Apr 25, 2023• 9 citations
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Abstract

Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing optical interferometers that could implement arbitrary transformations of input fields even in the case of high manufacturing errors. The building of detailed models of such devices drastically increases the efficiency of their practical use. The integral design of interferometers complicates its reconstruction since the internal elements are hard to address. This problem can be approached by using optimization algorithms [Opt. Express29, 38429 (2021)10.1364/OE.432481]. In this paper, we present what we believe to be a novel efficient algorithm based on linear algebra only, which does not use computationally expensive optimization procedures. We show that this approach makes it possible to perform fast and accurate characterization of high-dimensional programmable integrated interferometers. Moreover, the method provides access to the physical characteristics of individual interferometer layers.

DOI
10.1364/oe.487156

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Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing optical interferometers that could implement arbitrary transformations of input fields even in the case of high manufacturing errors. The building of detailed models of such devices drastically increases the efficiency of their practical use. The integral design of interferometers complicates its reconstruction since the internal elements are hard to address. This problem can be approached by using optimization algorithms [Opt. Express29, 38429 (2021)10.1364/OE.432481]. In this paper, we present what we believe to be a novel efficient algorithm based on linear algebra only, which does not use computationally expensive optimization procedures. We show that this approach makes it possible to perform fast and accurate characterization of high-dimensional programmable integrated interferometers. Moreover, the method provides access to the physical characteristics of individual interferometer layers.
Abstract Programmable linear optical interferometers are promising for classical and quantum applications. Their integrated design makes it possible to create more scalable and stable devices. To use them in practice, one has to reconstruct the whole device model taking the manufacturing errors into account. The inability to address individual interferometer elements complicates the reconstruction problem. A naive approach is to train the model via some complex optimization procedure. A faster optimization-free algorithm has been recently proposed (Bantysh et al 2023 Opt. Express 31 16729–42). However, it requires the full transfer matrix tomography while a more practical setup measures only the fields intensities at the interferometer output. In this paper, we propose the modification of the fast algorithm, which uses additional set of interferometer configurations in order to reconstruct the model in the case of intensity-only measurements. We show that it performs slightly worse than the original fast algorithm but it is more practical and still does not require intensive numerical optimization.
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.
Multimode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication and sensing, to computation, including optical neural networks, optical reservoir computing, or simulation of complex physical systems. The realization of such routines requires high levels of control and tunability of the parameters that define the operations carried out by the device. This requirement becomes particularly crucial in light of recent technological improvements in integrated photonic technologies, which enable the implementation of progressively larger circuits embedding a considerable amount of tunable parameters. We formulate efficient procedures for the characterization of optical circuits in the presence of imperfections that typically occur in physical experiments, such as unbalanced losses and phase instabilities in the input and output collection stages. The algorithm aims at reconstructing the transfer matrix that represents the optical interferometer without making any strong assumptions about its internal structure and encoding. We show the viability of this approach in an experimentally relevant scenario, defined by a tunable integrated photonic circuit, and we demonstrate the effectiveness and robustness of our method. Our findings can find application in a wide range of optical setups, based on both bulk and integrated configurations.
Linear-optical circuits are elementary building blocks for classical and quantum information processing with light. In particular, due to its monolithic structure, integrated photonics offers great phase-stability and can rely on the large scale manufacturability provided by the semiconductor industry. New devices, based on such optical circuits, hold the promise of faster and energy-efficient computations in machine learning applications and even implementing quantum algorithms intractable for classical computers. However, this technological revolution requires accurate and scalable certification protocols for devices that can be comprised of thousands of optical modes. Here, we present a novel technique to reconstruct the transfer matrix of linear optical networks that is based on the recent advances in low-rank matrix recovery and convex optimisation problems known as PhaseLift algorithms. Conveniently, our characterisation protocol can be performed with a coherent classical light source and photodiodes. We prove that this method is robust to noise and scales efficiently with the number of modes. We experimentally tested the proposed characterisation protocol on a programmable integrated interferometer designed for quantum information processing. We compared the transfer matrix reconstruction obtained with our method against the one provided by a more demanding reconstruction scheme based on two-photon quantum interference. For 5-dimensional random unitaries, the average circuit fidelity between the matrices obtained from the two reconstructions is 0.993.
Linear optical elements are pivotal instruments in the manipulation of classical and quantum states of light. Recent progress in integrated quantum photonic technology enabled the implementation of large numbers of such elements on chip, in particular passively stable interferometers. However, it is a challenge to characterize the optical transformation of such a device as the individual optical elements are not directly accessible. Thus only an effective overall transformation can be recovered. Here we present a reconstruction approach based on a global optimization of element parameters and compare it to two prominently used approaches. We numerically evaluate their performance for networks up to 14 modes and various levels of error on the primary data.
Tunable linear photonic circuits are important elements in both classical and quantum information technologies. The scaling of such circuits is possible only in the integrated form, which complicates their characterization because of the impossibility of the reconstruction of each element individually. The existing methods of characterization of linear photonic circuits require multiple changes in the phases of transfer matrix elements at various values of control parameters, which provides significant experimental difficulties. In this work, a new approach is proposed: it is demonstrated that the measurement of only transmission coefficients for certain values of the control parameters of the photonic circuit allows the development of a mathematical model that can predicts transmission coefficients for arbitrary values of the parameters. This method has been successfully approved in a numerical experiment for a tunable four-channel interferometer implementing an arbitrary unitary transformation. The proposed method provides new possibilities to efficiently characterize and design tunable linear photonic circuits.