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A combinatorial approach to quantum error correcting codes

German Luna

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4, Canada

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Samuel Reid

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4, Canada

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Bianca De Sanctis

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4, Canada

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, and

Vlad Gheorghiu

Department of Combinatorics and Optimizations, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada

Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada

Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada T2N 1N4, Canada

Institute for Quantum Science and Technology, University of Calgary, Calgary, AB, Canada T2N 1N4, Canada

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https://doi.org/10.1142/S1793830914500542Cited by:0 (Source: Crossref)

Abstract

Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric n-vertices colorable graph and a group of operations (coloring rules) on the graph: find the minimum sequence of operations that maps between two given graph colorings. We provide an explicit algorithm for computing the solution of our problem, which in turn is directly related to computing the distance (performance) of an underlying quantum error correcting code. Computing the distance of a quantum code is a highly non-trivial problem and our method may be of use in the construction of better codes.

Keywords:

AMSC: 94B25, 05C85, 81P70

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