Simulating Wigner Localisation with the IBM Heron 2 Quantum Processor: A Proof-of-Principle Benchmarking Study
Airat Kiiamov, Dmitrii Tayurskii
TL;DR
The study addresses simulating Wigner localisation in a quasi-1D electron system using digital quantum simulation. It maps a two-electron dimer onto a six-site ring with long-range Coulomb interactions and employs a variational quantum eigensolver (VQE) on the IBM Heron 2 processor with tunable couplers. Ground-state energies $E_G(U)$ are computed across $U \in [5,75]$ and benchmarked against exact diagonalisation, with error mitigation via Zero-Noise Extrapolation (ZNE) and Dynamical Decoupling (DD) achieving relative errors below 7% in the strong-coupling regime. The results demonstrate hardware-ready capability for probing strongly correlated phases and provide a baseline for scaling quantum simulations beyond the classical limit.
Abstract
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 \textbf{IBM\,Heron\,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 \textbf{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 \textbf{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.