 Clean subset superposition preparation

Suppose a known list of $2^m$ distinct $n$-bit strings $a_j$ is available and computational basis transpositions on $n+m$ qubits have polynomial-size implementations. Start with the uniform superposition state of index labels $j$, leaving the data zero. First swap $|0^n,j⟩$ with $|a_j,j⟩$ for each nonzero $a_j$. Next, for each $j\ne 0$, swap $|a_j,j⟩$ with $|a_j,0^m⟩$. Distinct index labels separate the first-stage pairs, and distinct data strings separate the second-stage pairs. Thus no later transposition disturbs an earlier term. At most $2^{m+1}-1$ transpositions prepare the uniform data state and return the quantum ancilla to zero. For $m=O(\log n)$ the quantum circuit has polynomial size. This assumes the list is available; a membership predicate alone does not supply it.