Use of Faulty States in Cat-Code Error Correction

TL;DR

This paper explores a teleportation-based approach to cat code quantum error correction, broadening the class of usable ancillary states and proposing bridge states for syndrome extraction under limited non-linear interactions.

Contribution

It introduces the use of many-component bridge states that enable syndrome extraction without requiring states to be in the cat code space.

Findings

Broader class of ancillary states for fault-tolerant correction.

Bridge states can perform syndrome extraction despite non-linear interaction limitations.

Enhances feasibility of cat code error correction in practical settings.

Abstract

Bosonic codes have seen a resurgence in interest for applications as varied as fault tolerant quantum architectures, quantum enhanced sensing, and entanglement distribution. Cat codes have been proposed as low-level elements in larger architectures, and the theory of rotationally symmetric codes more generally has been significantly expanded in the recent literature. The fault-tolerant preparation and maintenance of cat code states as a stand-alone quantum error correction scheme remains however limited by the need for robust state preparation and strong inter-mode interactions. In this work, we consider the teleportation-based correction circuit for cat code quantum error correction. We show that the class of acceptable ancillary states is broader than is typically acknowledged, and exploit this to propose the use of many-component ``bridge'' states which, though not themselves in the cat code space, are nonetheless capable of syndrome extraction in the regime where non-linear interactions are a limiting factor.