A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound

1996/04/29 by Daniel Gottesman · 1 voice · 146 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.1103/physreva.54.1862

published as Phys.Rev. A54 (1996) 1862 · REVTeX, 22 pages; introduction clarified and corrected to explicitly include non-orthogonal codes, claim of appendix A restricted to possibly allow some 1-error degenerate codes, references added; to appear in Phys. Rev. A

arxiv published 1996/04/29 · arxiv created 1996/07/24 · openalex publication_date 1996/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode k=n-j-2 qubits in n=2^j qubits and correct t=1 error.

Citations

• Good Quantum Error-Correcting Codes Exist

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Discussions

• Also no 'logical' when Gottesman introduced the stabilizer formalism a few days later. We simply encode k qubits in n qubits. arxiv.org/abs/quant-ph... [bsky, 3 points, 1 comments]

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