Iterative photonic processor for fast complex-valued matrix inversion

Abstract

An N × N iterative photonic processor is proposed for the first time, we believe, for fast computation of complex-valued matrix inversion, a fundamental but computationally expensive linear algebra operation. Compared to traditional digital electronic processing, optical signal processing has a few unparalleled features that could enable higher representational efficiency and faster computing speed. The proposed processor is based on photonic integration platforms–the inclusion of III-V gain blocks offers net neutral loss in the phase-sensitive loops. This is essential for the Richardson iteration method that is adopted in this paper for complex linear systems. Wavelength multiplexing can be used to significantly improve the processing efficiency, allowing the computation of multiple columns of the inverse matrix using a single processor core. Performances of the key building blocks are modeled and simulated, followed by a system-level analysis, which serves as a guideline for designing an N × N Richardson iteration processor. An inversion accuracy of > 98 % can be predicted for a 64 × 64 photonic processor with a > 80 times faster inversion rate than electronic processors. Including the power consumed by both active components and electronic circuits, the power efficiency of the proposed processor is estimated to be over an order of magnitude more energy-efficient than electronic processors. The proposed iterative photonic integrated processor provides a promising solution for future optical signal processing systems.

I/O-efficient iterative matrix inversion with photonic integrated circuits

“…The PIP generates matrix computation results one column at a time. Full-matrix inversion can be realised by using PIPs or by a multiplexing technique based on a different architecture we proposed 27 .…”

Chip-scale all-optical complex-valued matrix inverter

“…10 In addition, an iterative scheme combining photonic integration technologies and fiber loops has been proposed and verified to solve real-valued matrix inversion. 37,38 Limited by the large phase fluctuations, fiber-optic systems and free-space optical systems are only appropriate for real-valued calculations and exhibit a large system footprint. The utilization of integrated platforms has provided a novel methodology ARTICLE pubs.aip.org/aip/app for inverting complex-valued matrices.…”

Direct Iterative Photonic Integrated Matrix Inverter

“…Recently we have proposed an iterative photonic processor for fast matrix inversion computation, the detailed theoretical analyses being elaborated in [6]. In this paper, we present an experimental demonstration based on a silicon nitride (Si3N4) photonic integrated chip.…”