[QIP-Sem] QIP seminar, Mon 12/8, 4:15, 36-428, Zeng,Bei

[Peter Shor]

MIT Quantum Information Processing seminar
Monday 12/8 at 4:15 in 36-428
-------------------------------------------------

 Zeng,Bei (MIT)

Quantum Error Correction via Codes Over GF(3)

Abstract:

``Quantum Error Correction via Codes Over GF(4)" is one of the  seminal papers in quantum coding theory. This 1996 work transforms  the problem of finding binary quantum-error-correcting codes into  the problem of finding additive codes over the field GF(4) which are  self-orthogonal with respect to a certain trace inner product. Ever  since then, these codes, called additive codes or stabilizer codes,  have dominated the research on quantum coding theory. There is now a  rich theory of stabilizer codes, and a thorough understanding of  their properties. Nevertheless, there are a few known examples of nonadditive codes  which outperform any possible stabilzer code. In previous work, my  colleagues and I introduced the codeword stabilized quantum codes  framework for understanding additive and nonadditive codes. This has  allowed us to find, using exhaustive or random search, good new  nonadditive codes. However, these new codes have no obvious  structure to generalize to othe
 r cases. A systematical understanding  of constructing nonadditive quantum codes is still lacking. In this talk, we introduce the idea of constructing binary quantum- error-correcting codes via classical codes over the field GF(3).  Quantum codes directly constructed this way are nonadditive codes  adapted to the amplitude damping channel. These codes have higher  performance than all the previous codes for the amplitude damping  channel. We then further generalize this GF(3) idea to the case of  constructing 'usual' binary quantum codes for the depolarizing  channel, which leads to a systematical way of constructing good  nonadditive codes that outperform best additive codes. Using this  method, many good new codes are found. Particularly, we construct  families of good nonadditive codes which not only ourperform any  additive codes, but also asymptotically achieve the quantum Hamming  bound. Generalization to nonbinary case is straightforward and  families of good nonaddit
 ive nonbinary quantum codes are found. What  is more, our new method can also be used to construct additive  codes, and additive codes with better parameters than previous known  are found. Based on joint work with Markus Grassl, Peter Shor, Graeme Smith,  and John Smolin.

-------------------------------------------------
http://qis.mit.edu
http://mailman.mit.edu/mailman/listinfo/qip-sem