Topological approach toward quantum codes with realistic physical constraints

Details Topological approach toward quantum codes with realistic physical constraints Topological approach toward quantum codes with realistic physical constraints

2010-10-15

arxiv.org/abs/1010.3282v3

Physics

Quantum Physics

This paper has been withdrawn by the author. It is superseded by (and merged into) arXiv:1103.1885

Scientific paper

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.

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