Preparation of the single-spinon wave function in a quantum computer

We consider the preparation of single-spinon wave functions, relevant for one-dimensional $S=1/2$ spin models, in a quantum computer. We adopt the recently proposed ansatz \cite{kulk} for the single-spinon wave function, where a state with $S=1/2$ is built in a spin chain with $L+1$ sites, adding a site with $S_z=1/2$ to the configurations of the ground-state wave function for the spin chain with length $L$. We extend the original work to the case of the Haldane-Shastry model. We discuss how to prepare the single-spinon ansatz both for the Heisenberg and Haldane-Shastry models in quantum computers, using a linear combination of unitaries. We consider three different strategies to compute the single-spinon energy in a quantum computer and analyze their cost in terms of the number of qubits, gates, and circuits.