Earl T. Campbell, Hussain Anwar, Dan E. Browne
We propose families of protocols for magic state distillation -- important components of fault tolerance schemes --- for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that in higher dimensions smaller codes can be used than one might expect based on qubit codes. All our protocols produce magic states at a resource cost that increases only polynomially with the inverse of the final ouput error probability. We give specific details for 3-dimensional systems, where we find that certain magic states can be distilled provided an initial error probability of less than 20.02% or a depolarizing noise rate of less than 31.7%. This is the largest error probability threshold of all known protocols with polynomial resource cost. For a depolarizing noise model we also give distillation thresholds for odd prime dimensions up-to 19.
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http://arxiv.org/abs/1205.3104
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