  Finding the ground state energy and wavefunction of a quantum many-body
system is a key problem in quantum physics and chemistry. We study this problem
for the long-range XY model by using the variational quantum eigensolver (VQE)
algorithm. We consider VQE ansatzes with full and linear entanglement
structures consisting of different building gates: the CNOT gate, the
controlled-rotation (CRX) gate, and the two-qubit rotation (TQR) gate. We find
that the full-entanglement CRX and TQR ansatzes can sufficiently describe the
ground state energy of the long-range XY model. In contrast, only the
full-entanglement TQR ansatz can represent the ground state wavefunction with a
fidelity close to one. In addition, we find that instead of using
full-entanglement ansatzes, restricted-entanglement ansatzes where entangling
gates are applied only between qubits that are a fixed distance from each other
already suffice to give acceptable solutions. Using the entanglement entropy to
characterize the expressive powers of the VQE ansatzes, we show that the
full-entanglement TQR ansatz has the highest expressive power among them.
