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

TL;DR

This paper addresses the challenge of programming universal unitary transformations on a general-purpose silicon photonics platform with a hexagonal mesh of programmable unit cells (PUCs). It develops a META-MZI–based phase-calibration approach and demonstrates an equivalence between two concatenated PUCs and a Mach-Zehnder interferometer, enabling standard rectangular (Clements) and triangular (Reck) unitary architectures on the hexagonal hardware. Through extensive experiments programming 3×3 and 4×4 random unitary matrices, it achieves fidelities well above 98% and approximately 5.3–5.5 bit weight precision, validating coherent vector–matrix multiplications on a general-purpose photonic processor. The work further demonstrates applications in photonic neural networks and quantum gates, underscoring the platform’s potential for optical computing and signal processing, while outlining scalability and loss challenges and suggesting avenues for improvement via lower-loss PUCs and non-volatile phase technologies.

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.

Figures (10)

• Figure 1: a Smarlight processor from IPronics. It combines an hexagonal waveguide mesh with an electronic and software layer, and b Programmable unit cell (PUC) of the hexagonal mesh. It consist of two internal phase shifters $\theta_{1}$ and $\theta_{2}$.
• Figure 2: a 1x4 Symmetric splitter tree, and b 1x4 Non-symmetric splitter tree.
• Figure 3: a The standard building block consists of an MZI with one external and one internal phase shifter, b equivalent system that concatenates two PUCs with $\theta_{2}$ = 0 and $\phi_{1}$ = $\phi_{2}$.
• Figure 4: a Schematic of the Clements topology with its translation to the hexagonal mesh, and b schematic of the Reck topology with its translation to the hexagonal mesh.
• Figure 5: META-MZI method for the characterization of the passive phase of the phase shifters and its translation to the hexagonal mesh.