A Study of Entanglement and Ansatz Expressivity for the Transverse-Field Ising Model using Variational Quantum Eigensolver

TL;DR

This paper investigates how different ansatzes affect the ability of VQE to accurately simulate the transverse-field Ising model, focusing on entanglement and eigenstate preparation in various dimensions and system sizes.

Contribution

It provides a comparative analysis of ansatz expressivity and entanglement properties for VQE applied to the TFIM across multiple dimensions and system sizes.

Findings

Hardware-efficient ansatz struggles with highly entangled states.

Physics-inspired ansatz improves eigenstate fidelity.

Symmetry-breaking ansatz enhances accuracy in degenerate regimes.

Abstract

The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. Its effectiveness, however, depends on the faithful preparation of eigenstates, which becomes challenging in degenerate and strongly entangled regimes. We study this problem using the transverse-field Ising model (TFIM) with periodic boundary conditions in one, two, and three dimensions, considering systems of up to 27 qubits. We employ different ansatzes: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational Ansatz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization.