# Hybrid spatiotemporal architectures for universal linear optics

## TL;DR

This paper introduces hybrid linear-optical architectures that leverage both spatial and temporal light degrees of freedom to implement large-scale, arbitrary unitary transformations efficiently, combining advantages of existing methods.

## Contribution

The paper proposes novel hybrid architectures for linear optics that integrate spatial and temporal modes, enabling scalable and efficient quantum optical transformations.

## Key findings

- Hybrid architectures combine benefits of spatial and temporal linear optics.
- Decomposition methods for large unitaries are broadly useful.
- Hybrid approaches offer advantages over purely spatial or temporal systems.

## Abstract

We present two hybrid linear-optical architectures that simultaneously exploit spatial and temporal degrees of freedom of light to effect arbitrary discrete unitary transformations. Our architectures combine the benefits of spatial implementations of linear optics, namely low loss and parallel operation, with those of temporal implementations, namely modest resource requirements and access to transformations of potentially unbounded size. We arrive at our architectures by devising and employing decompositions of large discrete unitary transformations into smaller ones, decompositions we expect to have broad utility beyond spatio-temporal linear optics. We show that hybrid architectures promise important advantages over both spatial-only and temporal-only architectures.