  Neural-Network Quantum State (NQS) has attracted significant interests as a
powerful wave-function ansatz to model quantum phenomena. In particular, a
variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted
to model the ground state of spin lattices and the electronic structures of
small molecules in quantum devices. Despite these progresses, significant
challenges remain with the RBM-NQS based quantum simulations. In this work, we
present a state-preparation protocol to generate a specific set of
complex-valued RBM-NQS, that we name the unitary-coupled RBM-NQS, in quantum
circuits. This is a crucial advancement as all prior works deal exclusively
with real-valued RBM-NQS for quantum algorithms. With this novel scheme, we
achieve (1) modeling complex-valued wave functions, (2) using as few as one
ancilla qubit to simulate $M$ hidden spins in an RBM architecture, and (3)
avoiding post-selections to improve scalability.
