# Physical-depth architectural requirements for generating universal photonic cluster states

## TL;DR

This paper investigates the physical architectural constraints for generating universal photonic cluster states in linear-optical quantum computing, demonstrating that a fixed-depth device can achieve percolation and universality.

## Contribution

It introduces a model for fixed-depth physical architectures in LOQC and shows that universal cluster states can be generated without complex algorithms.

## Key findings

- Universal LOQC achievable with constant-size device
- Percolation maintained with simple pathfinding strategies
- Physical depth constraints do not prevent universal cluster state generation

## Abstract

Most leading proposals for linear-optical quantum computing (LOQC) use cluster states, which act as a universal resource for measurement-based (one-way) quantum computation (MBQC). In ballistic approaches to LOQC, cluster states are generated passively from small entangled resource states using so-called fusion operations. Results from percolation theory have previously been used to argue that universal cluster states can be generated in the ballistic approach using schemes which exceed the critical threshold for percolation, but these results consider cluster states with unbounded size. Here we consider how successful percolation can be maintained using a physical architecture with fixed physical depth, assuming that the cluster state is continuously generated and measured, and therefore that only a finite portion of it is visible at any one point in time. We show that universal LOQC can be implemented using a constant-size device with modest physical depth, and that percolation can be exploited using simple pathfinding strategies without the need for high-complexity algorithms.