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

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.

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