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Quantum Error Correction via Codes over GF(4)

1996/08/06 by A.R. Calderbank, A. R. Calderbank, Calderbank, A. R. +8
Computer Science · Physics and Astronomy · #Coding theory and cryptography #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9608006

Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor errors

openalex publication_date 1996/08/06 · arxiv created 1997/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.

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