Quantum simulation of the Hubbard model on a graphene hexagon: Strengths of IQPE and noise constraints

Quantum simulation of the Hubbard model on a graphene hexagon: Strengths of IQPE and noise constraints | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Quantum simulation of the Hubbard model on a graphene hexagon: Strengths of IQPE and noise constraints Mohammad Mirzakhani, Kyungsun Moon This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7369853/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Nov, 2025 Read the published version in EPJ Quantum Technology → Version 1 posted 13 You are reading this latest preprint version Abstract Quantum computing offers transformative potential for simulating real-world materials, providing a powerful platform to investigate complex quantum systems across quantum chemistry and condensed matter physics. In this work, we leverage this capability to simulate the Hubbard model on a six-site graphene hexagon using Qiskit, employing the Iterative Quantum Phase Estimation (IQPE) and adiabatic evolution algorithms to determine its ground-state properties. Our results show that a single Slater determinant is sufficient to initialize IQPE and accurately recover ground-state energies (GSEs) in small-scale Hubbard systems. In noiseless simulations, IQPE converges within a few iterations to exact GSEs, while adiabatic simulations yield charge and spin densities and correlation functions in excellent agreement with exact diagonalization. However, deploying IQPE and adiabatic evolution on today's noisy quantum hardware remains highly challenging. To investigate these limitations in IQPE, we use the Qiskit Aer simulator with a custom noise model tailored to the characteristics of IBM's real hardware. This model includes realistic depolarizing gate errors, thermal relaxation, and readout noise, allowing us to explore how these factors degrade simulation accuracy. Further, we implement the IQPE algorithm on IBM's ibm_strasbourg and ibm_fez devices for a reduced three-site Hubbard model, enabling direct comparison between simulated and real hardware noise. While ibm_fez runs closely match exact results, discrepancies highlight the gap between modeled and physical noise. This study demonstrates both the IQPE's potential and current limitations for simulating strongly correlated systems under realistic conditions. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 18 Nov, 2025 Read the published version in EPJ Quantum Technology → Version 1 posted Editorial decision: Revision requested 05 Sep, 2025 Reviews received at journal 02 Sep, 2025 Reviewers agreed at journal 01 Sep, 2025 Reviews received at journal 01 Sep, 2025 Reviewers agreed at journal 31 Aug, 2025 Reviewers agreed at journal 29 Aug, 2025 Reviewers agreed at journal 22 Aug, 2025 Reviewers agreed at journal 22 Aug, 2025 Reviewers agreed at journal 19 Aug, 2025 Reviewers invited by journal 19 Aug, 2025 Editor assigned by journal 19 Aug, 2025 Submission checks completed at journal 19 Aug, 2025 First submitted to journal 14 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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