Exploring variational circuit structures for efficient simulation of the long-range XY model

We investigate variational quantum eigensolver (VQE) ansatzes for simulating the ground state of the long-range XY model. We compare entanglers based on parametric controlled- \(Rₓ\) ( \(CRₓ\) ), \(Rₓₓ\) and combined \(Rₓₓ\) and \(Ryy\) rotations ( \(RₓₓRyy\) ), considering both homogeneous and inhomogeneous parameter-sharing schemes. Numerical simulations show that the mean-field ansatz reproduces the mean-field energy but fails to capture quantum correlations. Introducing entanglers reveals distinct trade-offs between expressibility and trainability. The inhomogeneous \(CRₓ\) ansatz yields accurate energies with shallow circuits, whereas the homogeneous \(Rₓₓ\) ansatz benefits from symmetry and a smoother optimization landscape. Notably, the \(RₓₓRyy\) ansatz delivers the highest fidelity across the entire phase diagram, with the inhomogeneous version achieving high accuracy using only two layers, and the homogeneous one also exhibiting good performance with moderate depth. These results underline the importance of tailoring ansatz structure and parameter sharing to the underlying Hamiltonian to enable efficient and accurate quantum simulation on near-term devices.