Programming universal unitary transformations on a general-purpose silicon photonics platform

TL;DR

This paper demonstrates the programming of universal unitary transformations on a silicon photonics platform, achieving high fidelity and bit precision, advancing the capabilities of programmable photonic processors for quantum and optical computing.

Contribution

It introduces a method to implement and calibrate universal unitary transformations on a hexagonal photonic mesh, a novel achievement for general-purpose programmable photonic circuits.

Findings

Achieved >98% fidelity in 3x3 and 4x4 unitary matrices

Demonstrated programmable matrix multiplication on the photonic platform

Recalibrated system to compensate for phase deviations

Abstract

General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach-Zehnder interferometers, these systems have demonstrated significant potential in microwave photonics applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach-Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3x3 and 4x4 random unitary matrices yields fidelities > 98% and bit precisions over 5 bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.