Freedman, Michael H.; Meyer, David A.; Luo, Feng \(Z_2\)-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]. Reviewer: Guy Jumarie (Montréal) Cited in 1 ReviewCited in 15 Documents MSC: 81P68 Quantum computation PDFBibTeX XMLCite \textit{M. H. Freedman} et al., in: Mathematics of quantum computation. Boca Raton, FL: Chapman \& Hall/ CRC. 287--320 (2002; Zbl 1075.81508)