# Robust fault tolerance for continuous-variable cluster states with excess anti-squeezing

## TL;DR

This paper demonstrates that excess anti-squeezing does not affect the fault-tolerance threshold in continuous-variable cluster states, simplifying experimental requirements for scalable quantum computing.

## Contribution

It shows that anti-squeezing has no impact on fault tolerance, removing the need for state purity and guiding experimental squeezing targets.

## Key findings

- Anti-squeezing does not influence fault-tolerance thresholds.
- Experimental focus should be on achieving 15-17 dB of squeezing.
- Purity requirements can be relaxed in fault-tolerant designs.

## Abstract

The immense scalability of continuous-variable cluster states motivates their study as a platform for quantum computing, with fault tolerance possible given sufficient squeezing and appropriately encoded qubits [Menicucci, PRL 112, 120504 (2014)]. Here, we expand the scope of that result by showing that additional anti-squeezing has no effect on the fault-tolerance threshold, removing the purity requirement for experimental continuous-variable cluster-state quantum computing. We emphasize that the appropriate experimental target for fault-tolerant applications is to directly measure 15-17 dB of squeezing in the cluster state rather than the more conservative upper bound of 20.5 dB.