×

zbMATH — the first resource for mathematics

\(Z_2\)-systolic freedom and quantum codes. (English) Zbl 1075.81508
Chen, Goong (ed.) et al., Mathematics of quantum computation. Boca Raton, FL: Chapman & Hall/ CRC (ISBN 1-58488-282-4). Computational Mathematics Series, 287-320 (2002).
The topology of CSS (Calderbank-Shor and Steane) codes can be realized in a geometrical setting in which there is a locality condition which requires that each stabilizer involves only a bounded number of Pauli matrices. It is shown that a suitable framework is provided by the Riemannian geometry of closed smooth manifold \(M^{d}\). In this unified approach one can answer two conjectures, one in differential geometry, and the other one in quantum information. Some definitions related to the notations are missing. For instance, \(S^{2}\times S^{1}\), what is it?
For the entire collection see [Zbl 1077.81018].

MSC:
81P68 Quantum computation
PDF BibTeX XML Cite