Scalar computational primitives with perturbative phase interferometry

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.