Low Overhead Qutrit Magic State Distillation

We construct a family of [9m-k, k, 2]₃ triorthogonal codes, for k≤ 3m-2, for qutrit magic state distillation with low overhead. The overhead cost of a magic state distillation routine is characterized by the yield parameter γ = logd ( n/k ). When $k=3m-2$, the codes have yield parameter γ = log₂ (2+6/3 m-2), which tends to $1$ as m → ∞. Moreover, the [20,7,2]₃ qutrit code that arises when $m=3$ already has a yield parameter of $1.51$ which outperforms all known qubit triorthogonal codes of size less than a few hundred qubits. We also find that the [17,1,2]₃ code distills magic states with a higher noise threshold than previously known qutrit triorthogonal codes.