Variational approach to photonic quantum circuits via the parameter shift rule

TL;DR

This paper develops a parameter shift rule tailored for photonic quantum circuits, enabling efficient gradient calculations and noise resilience, demonstrated through experimental variational algorithms on a reconfigurable integrated photonic platform.

Contribution

It introduces a novel parameter shift rule formulation for photonic circuits based on Boson Sampling, incorporating noise effects, and demonstrates its application in experimental variational algorithms.

Findings

Successful experimental implementation of variational algorithms on a 6-mode photonic interferometer.

Effective embedding of experimental noise into the derivative calculation.

Validation of the approach with eigensolver and Universal-Not gate tasks.

Abstract

In the era of noisy intermediate-scale quantum computers, variational quantum algorithms are promising approaches for solving optimization tasks by training parameterized quantum circuits with the aid of classical routines informed by quantum measurements. In this context, photonic platforms based on reconfigurable integrated optics are an ideal candidate for implementing these algorithms. Among various techniques to train variational circuits, the parameter shift rule enables the exact calculation of cost-function derivatives efficiently, facilitating gradient descent-based optimization. In this paper, we derive a formulation of the parameter shift rule for computing derivatives and integrals tailored to reconfigurable optical linear circuits and based on the Boson Sampling paradigm. This allows us to naturally embed common types of experimental noise, such as partial distinguishability and mixedness of the states, thus obtaining a resilient approach. Finally, we employ the developed approach to experimentally test variational algorithms with single-photon states processed in a reconfigurable 6-mode universal integrated interferometer. Specifically, we apply the photonic parameter shift rules to the variational implementation, on a photonic platform, of both an eigensolver and a Universal-Not gate.