Preparing multi-qudit states in a definite-weight subspace
The authors developed a deterministic algorithm to prepare arbitrary multi-qudit states within a definite-weight subspace by ordering basis states using a Gray code for multiset permutations. This reduces state preparation to controlled 2-qudit Gray rotations. The method successfully prepares exact eigenstates of the SU(3)-invariant Heisenberg Hamiltonian, including Bethe states and their lower-weight descendants, while also applying the technique to SU(d) Dicke and q-deformed Dicke states.