Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.
Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions.
Integrated photonics enabled the capability to implement complex interferometers with a large number of modes. The applications of this experimental toolbox can be found in different quantum information tasks, including quantum walks and simulation [1], quantum metrology [2], up to the implementation of Boson Sampling [3-6], one of the most promising candidates to reach experimentally the regime where a quantum device solves a computational problem faster than its classical counterpart. Both from a fundamental aspect and for characterization purposes, it becomes crucial to identify tools allowing to learn the action of an unknown transformation.
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.
Quantum metrology is one of the most relevant applications of quantum information theory to quantum technologies.Here, quantum probes are exploited to overcome classical bounds in the estimation of unknown parameters.In this context, phase estimation, where the unknown parameter is a phase shift between two modes of a quantum system, is a fundamental problem.In practical and realistic applications, it is necessary to devise methods to optimally estimate an unknown phase shift by using a limited number of probes.Here we introduce and experimentally demonstrate a machine learning-based approach for the adaptive estimation of a phase shift in a Mach-Zehnder interferometer, tailored for optimal performances with limited resources.The employed technique is a genetic algorithm used to devise the optimal feedback phases employed during the estimation in an offline fashion.The results show the capability to retrieve the true value of the phase by using few photons, and to reach the sensitivity bounds in such small probe regime.We finally investigate the robustness of the protocol with respect to common experimental errors, showing that the protocol can be adapted to a noisy scenario.Such approach promises to be a useful tool for more complex and general tasks where optimization of feedback parameters is required.
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our approach accounts for losses and photon indistinguishability, making it robust to experimental imperfections. By minimizing the requirements for the input states, the method simplifies the experimental implementation. We demonstrate the effectiveness of our technique through theoretical modeling and experimental validation in a 4-mode programmable integrated optical interferometer. The results show high fidelity in matrix reconstruction and successful application in boson sampling experiments. In addition, we provide a comprehensive formalism for correlation functions and discuss the robustness of the method to measurement errors. This work offers a practical and efficient solution for characterizing linear-optical networks, paving the way for scaling up photonic quantum technologies.
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.
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.