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Constructions and Noise Threshold of Hyperbolic Surface Codes

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An essential component of scalable quantum computing is the ability to reliably protect quantum information from decoherence. Such protection can in principle be achieved via the use of quantum error correcting codes.

We discuss a construction to obtain families of quantum codes based on regular tilings of surfaces with constant negative curvature. This construction results in two-dimensional quantum codes whose tradeoff between encoding rate and protection is more favorable than for the standard surface code.