Preparation of Hamming-Weight-Preserving Quantum States with Log-Depth Quantum Circuits

Hamming-Weight-Preserving (HWP) states, $\vertψ_{\mathrm{H}}\rangle=\sum_{\mathrm{HW}(x)=k}α_x\vert x\rangle$, represent a fundamental class of quantum states on $n$ qubits with fixed excitation number $k$, playing a pivotal role in quantum simulation, machine learning, and optimization, with promin