2012/05/31 by Earl T. Campbell, Hussain Anwar, Dan E. Browne · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevx.2.041021
published as Phys. Rev. X 2, 041021 (2012) · Updated from V1 to include results on the remarkable d=5 case
arxiv created 2012/07/19 · arxiv updated 2013/01/01
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.