Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches
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Quantum Physics arXiv:2601.17515 (quant-ph) [Submitted on 24 Jan 2026] Title:Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches Authors:Rudraksh Sharma View a PDF of the paper titled Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches, by Rudraksh Sharma View PDF HTML (experimental) 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. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.17515 [quant-ph] (or arXiv:2601.17515v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.17515 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rudraksh Sharma [view email] [v1] Sat, 24 Jan 2026 16:26:15 UTC (166 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Phase Transitions in the Transverse-Field Ising Model: A Comparative Study of Exact, Variational, and Hardware-Based Approaches, by Rudraksh SharmaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)