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

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.

arXiv comment6 pages, 4 figures, 2 tables

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Cited by in corpus (2)

• High-rate extended binomial codes for multiqubit encoding
• Quantum dual extended Hamming code immune to collective coherent errors