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

Yu Li, Guojing Tian, Xiaoyu He +3

Hamming-Weight-Preserving (HWP) states, $|{\psi }_{\mathrm{H}}⟩={\sum }_{\mathrm{HW}(x)=k}{\alpha }_x|x⟩$, represent a fundamental class of quantum states on $n$ qubits with fi…