Magic state distillation in all prime dimensions using quantum Reed-Muller codes
Abstract
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, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic state distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarising noise (36.3%) and the efficiency measure know as "yield", where, for a large region of parameters, it outperforms its qubit counterpart by many orders of magnitude.
Cite
@article{arxiv.1205.3104,
title = {Magic state distillation in all prime dimensions using quantum Reed-Muller codes},
author = {Earl T. Campbell and Hussain Anwar and Dan E. Browne},
journal= {arXiv preprint arXiv:1205.3104},
year = {2013}
}
Comments
Updated from V1 to include results on the remarkable d=5 case