Magic state distillation in all prime dimensions using quantum Reed-Muller codes

TL;DR

This paper introduces new magic state distillation protocols for odd prime-dimensional quantum systems using quantum Reed-Muller codes, achieving high efficiency and error thresholds, especially in five-dimensional systems.

Contribution

It develops novel protocols for magic state distillation in higher dimensions using quantum Reed-Muller codes with transversal non-Clifford gates, outperforming previous qubit-based schemes.

Findings

Five-dimensional protocol has a 36.3% error threshold.

The five-dimensional scheme outperforms qubit protocols in yield.

Small, effective codes are identified for higher-dimensional systems.

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.