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

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.