Lie algebraic techniques prove hardware-efficient gates are universal for state preparation in constrained subspaces, like those with fixed particle number or spin. This universality is achieved through Pauli $Z$ dressing, where commutators produce Pauli $Z$ operators acting as spectator projectors, decomposing multi-plane rotations into single-plane generators spanning the full $\mathfrak {so}(w)$ algebra, where $w$ is the dimension of the constrained subspace.
Pauli Z dressing unlocks universal quantum gates in limited spaces
Lie algebraic techniques prove hardware-efficient gates are universal for state preparation in constrained subspaces, like those with fixed particle number or spin. This universality is achieved through Pauli $Z$ dressing, where commutators produce Pauli $Z$ operators acting as spectator projectors, decomposing multi-plane rotations into single-plane generators spanning the full $\mathfrak {so}(w)$ algebra, where $w$ is the dimension of the constrained subspace.