Scalar computational primitives with perturbative phase interferometry

TL;DR

This paper demonstrates how weak phase modulations in modified linear interferometers can perform primitive computational tasks, leveraging phase parametrization to implement nonlinear operations with linear optics.

Contribution

It introduces a method to perform nonlinear computations using linear interferometers by exploiting phase perturbations and their nonlinear parametrization.

Findings

Linear interferometers can perform nonlinear operations like division and powers.

Operation accuracy improves with smaller input perturbations.

Phase changes are read out as optical power variations.

Abstract

We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the operations are enacted by moving from one state to another. This harnesses the particular phase parametrization of an interferometer, allowing entirely linear optics to produce nonlinear operations such as division and powers. This is due to the nonlinear structure of the underlying phase parametrizations. The realized operations are approximate but can be made more accurate by decreasing the size of the input perturbations. For each operation, the inputs and outputs are changes in phase relative to a fixed bias point. The output phase is ultimately read out as a change in optical power.