Quantum Decoding with Venn Diagrams

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to engineers. An illustrative example is presented of a naive perfect quantum code (Hamming-like code) with five-qubits for transmitting a single qubit of information. Also the (9,1)-Shor codes is addressed.

[1]  Viola,et al.  Theory of quantum error correction for general noise , 2000, Physical review letters.

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

[3]  N. Sloane,et al.  Quantum Error Correction Via Codes Over GF , 1998 .

[4]  N. Mermin Quantum Computer Science: An Introduction , 2007 .

[5]  Jehoshua Bruck,et al.  Decoding the Golay code with Venn diagrams , 1990, IEEE Trans. Inf. Theory.

[6]  N. J. A. Sloane,et al.  Quantum Error Correction Via Codes Over GF(4) , 1998, IEEE Trans. Inf. Theory.

[7]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[8]  Shu Lin,et al.  Channel Codes: Classical and Modern , 2009 .

[9]  Steane,et al.  Simple quantum error-correcting codes. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[10]  Hoang Pham,et al.  A note on the Venn and Ben diagrams , 1992 .

[11]  Markus Grassl,et al.  Quantum Reed-Solomon Codes , 1999, AAECC.

[12]  E. Knill,et al.  Theory of quantum error-correcting codes , 1997 .

[13]  Santosh Kumar,et al.  Nonbinary Stabilizer Codes Over Finite Fields , 2005, IEEE Transactions on Information Theory.

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

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

[16]  N. Sloane,et al.  Quantum error correction via codes over GF(4) , 1996, Proceedings of IEEE International Symposium on Information Theory.

[17]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[18]  Gregg Jaeger,et al.  A Short Introduction to Quantum Information and Quantum Computation , 2007 .

[19]  D. Marinescu,et al.  Classical and Quantum Information Theory , 2011 .

[20]  Hoi-Kwong Lo,et al.  Introduction to Quantum Computation Information , 2002 .

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

[22]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.