Ansätz Expressivity and Optimization in Variational Quantum Simulations of Transverse-field Ising Model Across System Sizes
arXiv:2604.20961
The paper studies how well the Variational Quantum Eigensolver can find ground‑state properties, especially entanglement entropy, of the transverse‑field Ising model in 1‑D, 2‑D, and 3‑D systems up to 27 spins, comparing several ansätze and analyzing expressivity and optimization performance.
Abstract
We explore the application of the Variational Quantum Eigensolver (VQE) to investigate the ground state properties, particularly the entanglement entropy, of the Transverse Field Ising Model (TFIM) in one, two, and three dimensions, considering systems of up to 27 spins. By benchmarking VQE results against exact diagonalization and analyzing the entanglement properties across different system sizes, we assess the algorithm's effectiveness in capturing faithful ground state. Using results of TFIM, we also investigate how VQE's expressivity and optimization influence the simulation of highly entangled quantum states. We employ different ansätze: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational ansätz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization. We further discuss the implications for scaling these methods to larger quantum systems.
26 pages, 11 figures, 2 tables