Adapting the Krishna–Tillich prime-dimensional qudit protocol to qubit magic state distillation

Determine how to adapt the Krishna–Tillich (2019) magic state distillation protocol for prime-dimensional qudits to distil magic states for qubits (dimension 2) using stabiliser operations, by providing an explicit construction that enables qubit magic state distillation within that framework.

Background

Krishna and Tillich (2019) showed that protocols based on triorthogonality over F_p for prime-dimensional qudits can achieve overhead exponents approaching zero, but their constructions inherently require increasing qudit dimension.

The present paper achieves constant-overhead magic state distillation for qubits via a different route that uses 2^10-dimensional qudits mapped to qubits; however, whether the Krishna–Tillich protocol itself can be adapted to the qubit setting remains unresolved and explicitly noted as unknown.