Simulating Wigner Localisation with the IBM Heron 2 Quantum Processor: A Proof-of-Principle Benchmarking Study

We report on a high-fidelity digital quantum simulation of Wigner localisation in a quasi-one-dimensional (quasi-1D) electron system using a 6-qubit segment of the state-of-the-art $\mathbf{\text{IBM}}\mathbf{\text{Heron}}\mathbf{\text{2}}$ quantum processor. By mapping the Coulomb interaction Hamiltonian onto a 6-qubit ring lattice, we reconstruct the ground-state energy landscape for a 2-electron Wigner dimer across fifteen interaction regimes in the range $U\in [5,75]$. This study serves as a rigorous $\mathbf{\text{benchmarking}}$ exercise, translating foundational experimental models originally developed for electrons on liquid helium into the domain of modern quantum computing. Leveraging the enhanced gate fidelity and tunable coupler architecture of the Heron 2, we demonstrate that the digital simulation accurately captures the energy minimisation trends associated with Wigner dimer formation, achieving a relative error below 7% in the strong-interaction limit. Our results provide a crucial $\mathbf{\text{proof-of-principle}}$ validation for using superconducting quantum hardware to probe strongly correlated phases of matter with high precision, establishing a baseline for future simulations beyond the classical limit.