A Variational Approach to Learning Photonic Unitary Operators

TL;DR

This paper introduces a variational method using structured light to learn high-dimensional optical unitary operators, achieving over 90% fidelity for dimensions up to 16, advancing quantum information processing capabilities.

Contribution

It presents a novel variational approach leveraging structured light and optical matrix-vector multiplication to learn high-dimensional unitary matrices experimentally.

Findings

Successfully learned unitary matrices for dimensions 2, 4, 8, 16

Achieved average fidelities greater than 90%

Demonstrated applicability to quantum state and process tomography

Abstract

Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to realise an adaptable scheme for learning unitary operations. Our approach borrows from concepts in variational quantum computing, where a search or optimisation problem is mapped onto the task of finding a minimum ground state energy for a given energy/goal function. We achieve this by a pseudo-random walk procedure over the parameter space of the unitary operation, implemented with optical matrix-vector multiplication enacted on arrays of Gaussian modes by exploiting the partial Fourier transforming capabilities of a cylindrical lens in the transverse degree of freedom for the measurement. We outline the concept theoretically, and experimentally demonstrate that we are able to learn optical unitary matrices for dimensions d = 2, 4, 8 and 16 with average fidelities of >90%. Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.