Scaling W State Circuits in the qudit Clifford Hierarchy
Lia Yeh · 2023
We identify a novel qudit gate which we refer to as the gate. This is an alternate generalization of the qutrit T gate to any odd prime dimension d, in the dth level of the Clifford hierarchy. Using this gate which is efficiently realizable fault-tolerantly should a certain conjecture hold, we deterministically construct in the Clifford+ gate set, d-qubit W states in the qudit {|0⟩, |1⟩} subspace. For qutrits, we show deterministic and fault-tolerant constructions for the three-qubit W state with T count three, for the six-qubit W state, and for any power-of-three-qubit W state.