[QIP-Sem] QIP seminar, Mon 3/17, 4:15pm, 36-428, Markus Grassl

[Peter Shor]

MIT Quantum Information Processing seminar
Monday 3/17 at 4:15pm in 36-428
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Markus Grassl (Innsbruck)

New families of non-additive quantum codes from Goethals and Preparata codes

Abstract:

Most of the quantum error-correcting codes (QECCs) are based on the stabilizer formalism which relates quantum codes to certain additive codes over GF(4).  However, it is known that non-additive QECCs can have a higher dimension compared to additive QECCs with the same length and minimum distance.  The most prominent example is the code ((5,6,2)) of Rains et al.  More recently, some improved one-error-correcting codes of length 9 and 10 have been found. So far, all these non-additive QECCs are obtained as the complex span of some stabilizer or graph states.

We extend the framework of stabilizer codes to the union of stabilizer codes which allows to construct non-additive codes from any stabilizer code.  Using constructions similar to those of CSS codes, families of non-additive quantum codes based on the binary Goethals and Preparata codes are presented.  In combination with Steane's enlargement construction, we obtain a family of non-additive quantum codes with parameters ((2m,22^m-5m+1,8)). The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance.

This is joint work with Martin Roetteler.

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