Low Overhead Qutrit Magic State Distillation

Abstract

We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of [[9m−k,k,2]]3 triorthogonal qutrit error-correcting codes for any positive integers m and k with k≤3m−2 that are suitable for magic state distillation. In magic state distillation, the number of ancillae required to produce a magic state with target error rate ϵ is O(logγ⁡ϵ−1), where the yield parameter γ characterizes the overhead cost. For k=3m−2, our codes have γ=log2⁡(2+63m−2), which tends to 1 as m→∞. Moreover, the [[20,7,2]]3 qutrit code that arises from our construction 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.