Optical modular arithmetic
Dmitri S. Pavlichin, Hideo Mabuchi

TL;DR
This paper introduces an optical circuit that performs phase-based arithmetic operations using nanoscale photonic devices, enabling ultra-low power computation for tasks like inner products and matrix operations.
Contribution
It proposes a novel optical circuit architecture for phase-based computation, extending to matrix operations and weighted readouts, utilizing coherence as a computational resource.
Findings
Demonstrates optical circuit for phase-based inner product computation
Extends to matrix-vector and matrix-matrix products
Potential applications in error correction and machine learning
Abstract
Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary "selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical…
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