Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches

• URL: http://arxiv.org/abs/2601.17515v1
• Date: Sat, 24 Jan 2026 16:26:15 GMT
• Title: Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches
• Authors: Rudraksh Sharma,
• Abstract summary: This paper will study the ground state properties and quantum critical dynamics of the one-dimensional transverse field Ising model.<n>We focus on a lattice of four spins, where we calculate the ground-state energies, magnetic order parameters and correlation functions.<n>We find that the ground-state energies of shallow variational circuits are reliably captured by the circuit over the entire parameter space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the one-dimensional transverse field Ising model through a combined perspective that includes exact diagonalisation, variational quantum eigensolver (VQE) simulations, and simulations on realistic physical quantum devices. We focus on a lattice of four spins, where we calculate the ground-state energies, magnetic order parameters and correlation functions at uniformly applied conditions, which is repeated by all systems. Precise diagonalisation provides both a benchmark, which is symmetry-conserving, and a depth-two, physics inspired variational approximation, which provides simulations accessible to hardware. The circuits that have been optimised identically are then placed on the IQM Garnet quantum processor, using a resource-efficient batched protocol. We find that the ground-state energies of shallow variational circuits are reliably captured by the circuit over the entire parameter space; the magnetic arrangement parameters and observables sensitive to correlation signal significantly more noise. The error analysis of quantitative analysis reveals a strong broadening of critical crossover on hardware, which is consistent with the noise attenuation of long-range correlations. These findings highlight the current capabilities as well as the fundamental limitations of noisy intermediate-scale quantum systems in modelling quantum critical phenomena as a benchmark to future enhancements in obtaining quantum hardware and quantum algorithms development.

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