Magic State Distillation with the Ternary Golay Code

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 distill 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 distills the “second-most magic” qutrit state, the Norell state, with quadratic error-suppression and an equally high threshold to depolarizing noise.