Native QR Factorization on Programmable Photonic Meshes
S. A. Fldzhyan, S. S. Straupe, M. Yu. Saygin
备注：
We have made substantial revisions to the manuscript. The asymptotic complexity is now improved by using a logarithmic tree concentrator. The basic self-configuring 2x2 block is now described more explicitly. Another addition is a new section that discusses the comparison with systolic arrays and describes blocked decomposition
We propose a photonic native procedure for computing the QR factorization of a matrix using a programmable unitary interferometer mesh. The method configures the mesh through a sequence of local power routing steps within tunable two mode interferometric elements, while reading out the resulting upper triangular factor directly from the optical outputs. The number of physical operations grows as $ O(N\log_2N)$ with matrix size $N$, reducing the runtime relative to standard digital QR routines, which scale cubically ($O(N^3)$). Beyond single factorizations, the same architecture supports iterative spectral computations by reusing the configured interferometer in a mirrored arrangement that implements the core update step of the QR eigenvalue algorithm. We also describe related optical procedures for Hessenberg reduction and bidiagonalization, serving as compatible preprocessors for QR and SVD workflows. A comparison with the systolic array computational architecture is provided. Our approach exhibits comparable asymptotic complexity for blocked QR decomposition and is more efficient for Hessenberg reduction and bidiagonalization.
The advances in fabrication processes in different material platforms employed in integrated optics are opening the path towards the implementation of circuits with increasing degree of complexity. In addition to the more conventional Application Specific Photonic Circuit (ASPIC) paradigm the Programmable Multifunctional Nanophotonics (PMN) approach is a transversal concept inspired by similar approaches, which are already employed in other technology fields. For instance, in electronics Field Programmable Gate Array (FPGA) devices enable a much more flexible universal operation as compared to…
Free-space optics (FSO) offer promising solutions in wireless systems where many different devices need to communicate and interoperate, exchanging massive amounts of data as in communication and sensor networks, and in technologies for positioning and ranging. In these applications, control and manipulation of the light field is required for properly generating and correctly receiving FSO beams even in the presence of unpredictable objects and turbulence in the light path. In this work, we use a programmable mesh of Mach-Zehnder Interferometers (MZIs) to automatically control the complex fiel…
Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler -- the Mach-Zehnder interferometer (MZI) -- cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer decreases with mesh size, allowing scaling to arbitrarily large m…
Universal Neural Network Based Calibration and Control of Programmable Classical and Quantum Photonic Integrated Processors
Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay（纳米科学与纳米技术研究中心，法国国家科学研究中心，巴黎萨克雷大学）；Centre for Nanophotonics, Department of Physics, Engineering Physics and Astronomy, Queen’s University（量子大学纳米光子学中心）；IPronics Programmable Photonics S.L（IPronics可编程光子有限公司）；Photonics Research Lab, iTEAM, Universitat Politècnica de València（瓦伦西亚理工大学iTEAM研究所光子研究实验室）
The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel blocks, however, the schemes turn out to be sensitive to fabrication errors. We study a novel decomposition method based on multi-channel blocks. We have shown that the scheme is universal even when the block`s transfer matrices are chosen at random, making it virtually insensitive to errors. Moreover, the placement of the variable elements can be arbitrary…
Adaptable, reconfigurable and programmable are key functionalities for the next generation of silicon-based photonic processors, neural and quantum networks. Phase change technology offers proven non-volatile electronic programmability, however the materials used to date have shown prohibitively high optical losses which are incompatible with integrated photonic platforms. Here, we demonstrate the capability of the previously unexplored material Sb$_2$Se$_3$ for ultralow-loss programmable silicon photonics. The favorable combination of large refractive index contrast and ultralow losses seen i…
Programmable pixel-mode linear interferometers using multi-plane light conversion
Department of Electrical and Computer Engineering, University of Maryland, College Park MD（马里兰大学电气与计算机工程系）；Wyant College of Optical Sciences, University of Arizona, Tucson AZ（亚利桑那大学瓦扬光学学院）
Linear light processing functions (e.g., routing, splitting, filtering) are key functions requiring configuration to implement on a programmable photonic integrated circuit (PPIC). In recirculating waveguide meshes (which include loop-backs), this is usually done manually. Some previous results describe explorations to perform this task automatically, but their efficiency or applicability is still limited. In this paper, we propose an efficient method that can automatically realize configurations for many light processing functions on a square-mesh PPIC. At its heart is an automatic differenti…
An optical equivalent of the field-programmable gate array (FPGA) is of great interest to large-scale photonic integrated circuits. Previous programmable photonic devices relying on the weak, volatile thermo-optic or electro-optic effect usually suffer from a large footprint and high energy consumption. Phase change materials (PCMs) offer a promising solution due to the large non-volatile change in the refractive index upon phase transition. However, the large optical loss in PCMs poses a serious problem. Here, by exploiting an asymmetric directional coupler design, we demonstrate PCM-clad sil…
Multiport interferometers based on integrated beamsplitter meshes have recently captured interest as a platform for many emerging technologies. In this paper, we present a novel architecture for multiport interferometers based on the Sine-Cosine fractal decomposition of a unitary matrix. Our architecture is unique in that it is self-similar, enabling the construction of modular multi-chiplet devices. Due to this modularity, our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of our circuit enables sy…
Recent breakthroughs in photonics-based quantum, neuromorphic and analogue processing have pointed out the need for new schemes for fully programmable nanophotonic devices. Universal optical elements based on interferometer meshes are underpinning many of these new technologies, however this is achieved at the cost of an overall footprint that is very large compared to the limited chip real estate, restricting the scalability of this approach. Here, we consider an ultracompact platform for low-loss programmable elements using the complex transmission matrix of a multi-port multimode waveguide.…
