Non-binary unitary error bases and quantum codes

Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed form linear codes over {ital Z}{sub {ital n}} for any {ital n}. The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.

[1]  Raymond Laflamme,et al.  Concatenated codes for fault tolerant quantum computing , 1995 .

[2]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[3]  Raymond Laflamme,et al.  Concatenated Quantum Codes , 1996 .

[4]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[5]  A. Steane.  Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  E. Knill.  Group representations, error bases and quantum codes , 1996, quant-ph/9608049.

[7]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[8]  Schumacher,et al.  Sending entanglement through noisy quantum channels. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[9]  Raymond Laflamme,et al.  A Theory of Quantum Error-Correcting Codes , 1996 .

[10]  A. Calderbank,et al.  Quantum Error Correction and Orthogonal Geometry , 1996, quant-ph/9605005.