High-Rate Amplitude-Damping Shor Codes with Immunity to Collective Coherent Errors

TL;DR

This paper presents a new family of high-rate quantum error-correcting codes that effectively correct amplitude-damping errors and are resilient to collective coherent errors, using structured stabilizer measurements for efficient error detection.

Contribution

Introduction of flexible, high-rate amplitude-damping Shor codes with approximate error correction and immunity to collective coherent errors, utilizing structured stabilizer measurements for efficiency.

Findings

Codes can approximately correct up to w amplitude-damping errors

Codes maintain immunity to collective coherent errors

Efficient local error detection using structured stabilizer measurements

Abstract

We introduce a family of high-rate amplitude-damping (AD) Shor Codes, designed to effectively correct AD errors while maintaining immunity to collective coherent (CC) errors. The proposed $[[(w+1)(w+K), K]]$ AD codes can approximately correct up to $w$ AD errors, with flexible parameters $(w, K)$, and we provide a rigorous proof that these codes satisfy the approximate quantum error correction conditions. These codes leverage structured stabilizer measurements, enabling efficient detection of AD errors using only local operations and ancillary qubits. We further construct a family of CC-AD Shor codes by concatenating these AD codes with the dual-rail code.