The loss tolerance of cat breeding for fault-tolerant grid state generation

TL;DR

This paper introduces a new simulation method for analyzing the loss tolerance of cat breeding protocols in fault-tolerant quantum state generation, revealing that loss above 4% impedes fault-tolerance.

Contribution

The authors develop an efficient Gaussian mixture-based simulation technique for GKP state preparation under loss, enabling rapid analysis of protocol performance.

Findings

Loss decreases success probability of the protocol.

Loss above 4% prevents fault-tolerant GKP state preparation.

Open-source code for the simulation method is provided.

Abstract

The development of a continuous-variable photonic quantum computer depends on the reliable preparation of high-quality Gottesman-Kitaev-Preskill states. The most promising GKP preparation scheme is the cat breeding protocol, which can generate GKP states deterministically given a source of squeezed cat states, using beam splitters, homodyne detectors and a feedforward displacement. However, analyzing the performance of the protocol under loss is cumbersome due to the exponential scaling of the system. By representing the Wigner function of the input states as a linear combination of Gaussians, we are able to quickly and accurately simulate several rounds of breeding with mixed input states. Using this novel method, we find that optical loss decreases the overall success probability of the protocol, and prohibits the preparation of a fault-tolerant GKP state when the loss exceeds 4\%. Our methodology is available as open-source code.