Magic state distillation with the ternary Golay code

Abstract

The ternary Golay code-one of the first and most beautiful classical error-correcting codes discovered-naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distil the 'most magic' qutrit state-an eigenstate of the qutrit Fourier transform known as the strange state-with cubic error suppression and a remarkably high threshold. It also distils the 'second-most magic' qutrit state, the Norell state, with quadratic error suppression and an equally high threshold to depolarizing noise.

Keywords: error correcting codes; fault-tolerant quantum computing; magic state distillation; quantum error correction.