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arXiv:2304.06486 · Advanced Photonics Nexus

Characterization of multimode linear optical networks

Francesco Hoch, Taira Giordani, Nicolò Spagnolo, Andrea Crespi, Roberto Osellame, Fabio Sciarrino

Published Jan 3, 2023• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1117/1.apn.2.1.016007

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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.
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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.
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.
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.
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.