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Quantum error correction via codes over GF(4)

IEEE Transactions on Information Theory · 1998 · Vol. 44(4) · pp. 1369–1387

A.R. Calderbank✉(AT&T (United States))Eric M. Rains(AT&T (United States))Peter Shor(AT&T (United States))N. J. A. Sloane(AT&T (United States))

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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.

Coding theory and cryptography Quantum Computing Algorithms and Architecture Quantum-Dot Cellular AutomataBlock codeLinear codeConcatenated error correction codeQubitMathematicsQuantum convolutional codeHamming codeError detection and correctionTornado codeFinite field

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Theory of fault-tolerant quantum computation