# Deterministic generation of a two-dimensional cluster state

## TL;DR

This paper presents a scalable, deterministic method for generating large two-dimensional photonic cluster states using temporal multiplexing, enabling universal measurement-based quantum computation with potential for fault tolerance.

## Contribution

A novel scheme utilizing temporal multiplexing, delay loops, and beam-splitters to produce large 2D cluster states suitable for universal quantum computing.

## Key findings

- Generated over 30,000 entangled modes in a cylindrical lattice
- Achieved a 1250-mode-long cluster state for deep quantum circuits
- Demonstrated potential for fault-tolerant quantum computation

## Abstract

Measurement-based quantum computation offers exponential computational speed-up via simple measurements on a large entangled cluster state. We propose and demonstrate a scalable scheme for the generation of photonic cluster states suitable for universal measurement-based quantum computation. We exploit temporal multiplexing of squeezed light modes, delay loops, and beam-splitter transformations to deterministically generate a cylindrical cluster state with a two-dimensional (2D) topological structure as required for universal quantum information processing. The generated state consists of more than 30000 entangled modes arranged in a cylindrical lattice with 24 modes on the circumference, defining the input register, and a length of 1250 modes, defining the computation depth. Our demonstrated source of 2D cluster states can be combined with quantum error correction to enable fault-tolerant quantum computation.