Methods of finding good quantum error-correcting codes are discussed, and many example codes are presented. The recipe ${\mathit{C}}_2^{\mathrm{\perp }}$⊂${\mathit{C}}_1$, where ${\mathit{C}}_1$ and ${\mathit{C}}_2$ are classical codes, is used to obtain codes for up to 16 information quantum bits (qubits) with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing ${\mathit{C}}_1$ to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error-correcting codes for 3, 4, and 5 information qubits with block lengths of 8, 10, and 11 qubits, respectively. © 1996 The American Physical Society.

• Received 15 May 1996

DOI:https://doi.org/10.1103/PhysRevA.54.4741