Quantum Error Correction and Orthogonal Geometry

Abstract

A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.

RevTex, 4 pages, no figures, submitted to Phys. Rev. Letters. We have changed the statement of Theorem 2 to correct it -- we now get worse rates than we previously claimed for our quantum codes. Minor changes have been made to the rest of the paper

References in corpus (6)

• Mixed State Entanglement and Quantum Error Correction
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Good Quantum Error-Correcting Codes Exist
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