Effective programming of a photonic processor with complex interferometric structure
I. V. Kondratyev, Kseniia N. Urusova, Artem S. Argenchiev, Nikita S. Klushnikov, Sergei S. Kuzmin, Nikolay N. Skryabin, Alexander D. Golikov, Vadim V. Kovalyuk, Gregory N Gol'tsman, I. V. Dyakonov, Stanislav S. Straupe, S. P. Kulik
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.
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.
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
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach-Zehnder interferometers, these systems have demonstrated significant potential in microwave photonics applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach-Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3x3 and 4x4 random unitary matrices yields fidelities > 98% and bit precisions over 5 bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.
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.
General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach–Zehnder interferometers, these systems have demonstrated significant potential in microwave photonic applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach–Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3 × 3 and 4 × 4 random unitary matrices yields fidelities >98% and bit precisions over five bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.
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.
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.