We present a simulated model to study the characterization of arbitrary unitary matrices implemented in an NxN integrated photonic Mach–Zehnder interferometer (MZI) mesh. We extend the measurement method of Hoch et al., which itself generalizes Liang et al., for the practical characterization of an arbitrary unitary transformation, U, implemented on such devices as an equivalent real bordered form Urb. The measurement scheme and reconstruction shown here require fewer and simpler measurements than Liang et al. and are more complete than Hoch et al. Completing the method of Hoch using our hybrid greedy-Tabu and Breadth First Search (BFS) algorithm makes our scheme practical in the sense that only simple classical resources are needed. This allows for practical characterization of the phases of Urb outside of a laboratory setting. We examine the performance of our reconstruction under simulated measurement noise and its scaling in time as a function of system size N.
We present a simulated model to study the characterization of arbitrary unitary matrices implemented in an NxN integrated photonic Mach–Zehnder interferometer (MZI) mesh. We extend the measurement method of Hoch et al., which itself generalizes Liang et al., for the practical characterization of an arbitrary unitary transformation, U, implemented on such devices as an equivalent real bordered form Urb. The measurement scheme and reconstruction shown here require fewer and simpler measurements than Liang et al. and are more complete than Hoch et al. Completing the method of Hoch using our hybrid greedy-Tabu and Breadth First Search (BFS) algorithm makes our scheme practical in the sense that only simple classical resources are needed. This allows for practical characterization of the phases of Urb outside of a laboratory setting. We examine the performance of our reconstruction under simulated measurement noise and its scaling in time as a function of system size N.
In this proceeding, we describe a simulated model for the characterization of arbitrary unitary matrices implemented by an reconfigurable linear optical network. We build on the method of Hoch et. al, which itself builds on Liang et. al, for characterizing the arbitrary unitary transformation, U, implemented on such devices as an equivalent real bordered form Urb. We disscuss how the measurement scheme requires fewer and simpler measurements than. We describe a solution that utilizes a novel algorithm to efficiently recover the complex signs of Urb under measurement noise and scaling with system size N.
There has been an escalating demand for dynamically reconfigurable photonic structures to implement any linear optical transformation between the input and output ports. Such devices are often constructed as a mesh of reconfigurable Mach-Zehnder interferometers(MZIs). Consequently, the programmed MZIs can redistribute the light to implementarbitrary unitary transformations from an input vector of optical signals to an outputvector of coherent optical modes. These structures have been widely used as a promising hardware platform for fast and energy-efficient matrix multiplications in different applications, such as information processing, machine learning algorithms, neural networks(NNs), etc. Matrix multiplication is an essential but time- and energy-consuming operation in machine learning computations. The computational complexity of NNs necessitates well designed and implemented hardware accelerators for fast and energy-efficient data processing, which allows for scaling the structure to larger NNs in current and upcoming applications. Over the last few years, the considerable progress in silicon photonics has made it possible to fabricate multiport optical interferometric structures with small ootprints and high-power efficiency, which can be exploited as hardware accelerators, thanks to the inherent parallelism of optics. This Ph.D. thesis presents the theoretical and experimental analysis of multiport reconfigurable MZI-based optical processors. The optical processors are meshes of 2×2 reconfigurable MZIs. It is demonstrated how the optical transformation matrix of the optical processors is theoretically decomposed for a given application. The Reck-mesh-based optical processor is experimentally calibrated before programming the device for a given application. Additionally, the thesis includes the theoretical and measurement results of a single layer NN implemented by a 4×4 Reck-mesh-based optical processor. Finally, a novel phase-error- and loss-tolerant multiport field-programmable MZI-based optical processor for optical NNs is proposed. The new structure with a diamond mesh shape makes use of a set of additional MZIs compared to the commonly used Reck (triangular) mesh. The additional MZIs in the Diamond mesh make its topology more symmetric yielding higher phase error- and loss-tolerance, and also provide extra degrees of freedom in the optimization of ONN weight matrix during training. Furthermore, the better classification performance of the Diamond mesh compared to the Reck mesh is associated with the fact that the Diamond mesh is capable of excluding the light intensity that could have degraded the classification accuracy of the implemented ONNs. This is done by means of the tapered-out wave guides of the additional MZIs in the Diamond mesh, while the optimal light intensity is sent to its outputs for better classification. The demonstration of these analyses is significant as it can be used to implement any universal field-programmable photonic device as an optical processor, i.e., optical computational accelerator, which can be experimentally programmed to implement arbitrary linear optical transformation matrix for a given application. Additionally, the presented analytical results in this thesis can be used to enhance the classification performance of ONNs implemented by such structures. As a result of these analyses, the thesis proposes the Diamond-mesh-based optical processor as a promising candidate for large scale ONNs which outperforms the Reck-mesh-based ones in the presence of experimental imperfections
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.
Programmable photonic interferometer meshes enable reconfigurable linear optical transformations, but their performance depends critically on accurate calibration of Mach-Zehnder interferometers and phase shifters. Conventional methods often require node isolation, dedicated routing paths, orthogonal training states, reference channels, or prior phase-voltage characterization, which become increasingly difficult in large thermally tuned meshes.
We introduce a local variance-based self-calibration method using intensity-only measurements. Controlled phase perturbations are applied, and calibration points are identified from minima of the measured output-power variance. For Mach-Zehnder interferometers, the variance follows a characteristic |sin(theta)| dependence, allowing bar and cross operating points to be found without conventional node isolation. For phase shifters, balanced interference produces a complementary |cos(phi)| variance signature, enabling quadrature calibration through the same statistical principle.
We validate the method experimentally on an 8 x 8 silicon nitride programmable photonic processor using a fully automated two-stage procedure. Starting from random phase settings, all Mach-Zehnder interferometers are calibrated first, followed by phase-shifter calibration under balanced-interference conditions. As a system-level test, we implement an embedded 4 x 4 Hadamard transformation on the 8 x 8 processor using a Clements decomposition.
These results establish local output variance as a simple calibration observable for programmable photonic meshes. The method is compatible with discrete random phase ensembles and requires neither conventional node isolation nor orthogonal training fields, making it a practical calibration primitive for scalable self-stabilizing photonic processors.
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 photonic devices comprised of simple beamsplitters and phase shifters can implement any unitary operator for quantum information processing. The significant practical challenge is to characterize such an interferometric device once it is built. Performing quantum process tomography requires the full suite of quantum tools such as N-mode quantum state preparation and measurement, and is, despite progress on more efficient methods, slow and impractical for large interferometric devices. Here we introduce a simple technique to characterize the unitary matrix of a linear photonic device using standard laser sources and photodetectors, without the requirement for active locking or single-photon sources. Our method is precise and efficient, requiring only 2N-1 measurement configurations for a N-path network. We use it experimentally to characterise an integrated 3x3 fused-fibre coupler and highlight its precision by comparing measured quantum interference patterns with those predicted using the classically-estimated unitary. We observe excellent agreement between the two experimental methods.