IBM Heron 2 Achieves High-Fidelity Simulation of Wigner Localisation with 6 Qubits

Wigner localisation, a phenomenon where electrons avoid each other due to electrostatic repulsion, has long been a cornerstone of condensed matter physics. Airat Kiiamov and Dmitrii Tayurskii, both from Kazan Federal University, alongside their colleagues, have now digitally simulated this effect using the IBM Heron 2 quantum processor. Their work maps the behaviour of electrons in a quasi-one-dimensional system onto a six-qubit ring lattice, successfully reconstructing the energy landscape of a two-electron Wigner dimer across a range of interaction strengths. This research is significant as it translates established experimental models into the realm of quantum computing, providing a crucial proof-of-principle demonstration of superconducting hardware’s ability to accurately model strongly correlated quantum systems. Achieving a relative error of less than 7%, the team establishes a vital baseline for future quantum simulations that venture beyond the capabilities of classical computers.

The study of this spontaneous transition into a spatially ordered configuration represents one of the most fundamental and enduring challenges in the field. First postulated by Eugene Wigner in 1934, it occurs in low-density regimes where Coulomb repulsion dominates over kinetic energy.

In such systems, the phase state is governed by the competition between repulsive potential energy and the delocalising influence of quantum zero-point fluctuations. When repulsion becomes sufficiently strong, electrons overcome their kinetic energy and form a spatially periodic configuration, known as a Wigner crystal or, for few-particle systems, a Wigner molecule. While the theoretical framework is well-established, experimental observation in a “clean” environment remains difficult due to disorder in traditional semiconductor platforms.

Historically, the most pristine realisations of Wigner systems have been achieved using electrons trapped on the surface of liquid helium. Unlike semiconductor heterostructures hindered by lattice defects, the surface of liquid helium at temperatures below 1 K is atomically smooth and virtually free of disorder. This provides a “pure” laboratory for observing correlation-driven phenomena in a quasi-one-dimensional electron gas. Researchers utilise microchannel devices to precisely control system geometry, reaching regimes where the number of electron rows is restricted, allowing study of collective dynamics and structural order.

A central theme of modern research is the transition from a classical electrostatic description to a fully quantum-mechanical one. Traditional low-density limits, where inter-electron distance is large, are often accurately modeled using classical mechanics and Molecular Dynamics simulations. However, as electrons are confined into smaller geometries, such as the electron dimer configurations studied in microchannels, the classical approximation becomes insufficient. Quantum phenomena like wave-function overlap, tunneling dynamics, and zero-point fluctuations emerge, fundamentally redefining the energy landscape and the stability of the localised phase.

Digital Quantum Simulation offers a promising alternative for probing these strongly correlated regimes. This study is positioned within the emerging framework of quantum utility and benchmarking, with the introduction of the IBM Heron 2 processor, featuring tunable couplers and enhanced gate fidelities. The team’s 6-site model serves as a vital proof-of-principle testbed for this new generation of hardware. While the Hilbert space dimension of 15 is classically tractable, this tractability is deliberate, allowing rigorous evaluation of the Heron 2 architecture’s ability to handle long-range correlations and suppress crosstalk before scaling to larger lattices.

To bridge the gap between continuous systems and digital simulation, the researchers model a 2-electron dimer confined to a 6-site ring, capturing the essential physics of structural order identified in previous research while eliminating edge effects through cyclic boundary conditions. The choice of six sites for two electrons yields a Hilbert space dimension of 15, enabling unambiguous benchmarking against classical exact diagonalisation. The system is described by a second-quantized Hamiltonian mapped onto a 6-site lattice with periodic boundary conditions, incorporating both a kinetic term favouring delocalisation and an interaction term accounting for the full long-range Coulomb profile.

The potential is calculated as the Coulomb interaction between electrons at each site, accurately reflecting the physical interactions within the Wigner crystal. Ground state energies were calculated using exact diagonalisation, and the model accurately captures the interplay between kinetic energy and Coulomb repulsion.

Wigner Dimer Simulation on Quantum Hardware

Scientists achieved a high-fidelity digital simulation of Wigner localisation, utilising a 6-qubit segment of the state-of-the-art Heron 2 processor. The research team mapped the Coulomb interaction Hamiltonian onto a 6-qubit ring lattice, reconstructing the ground-state energy landscape for a 2-electron Wigner dimer across fifteen interaction regimes. This work translates established experimental models, originally developed for electrons on liquid helium, into the domain of modern quantum computing, serving as a rigorous benchmarking exercise for the new hardware.

Experiments revealed accurate capture of the energy minimisation trends associated with Wigner dimer formation, demonstrating a relative error below 7% in the strong-interaction limit. The team modelled a 2-electron dimer confined to a 6-site ring, yielding a Hilbert space dimension of 15, allowing for direct comparison with classical exact diagonalisation techniques. A second-quantized Hamiltonian was employed, incorporating both a kinetic term representing electron tunneling and a crucial interaction term accounting for long-range Coulomb interactions between all pairs of sites.

This long-range interaction is essential for accurately modelling the electrostatic energy landscape driving dimer formation. Measurements confirm the successful implementation of a Variational Quantum Eigensolver on the Heron 2 processor to determine the ground-state energy, optimised using the COBYLA algorithm. The Hamiltonian incorporates the chord distance to calculate the potential between sites on a unit circle, accurately reflecting the collective repulsion between electrons. This detailed modelling allows for precise simulation of the antipodal positioning of electrons observed in the strong-interaction limit.

The breakthrough delivers a crucial proof-of-principle validation for utilising superconducting quantum hardware to probe strongly correlated phases of matter with high precision. Tests prove the Heron 2 architecture’s ability to handle long-range correlations and suppress crosstalk, establishing a baseline for future simulations extending beyond the capabilities of classical computation. This study positions the research within the emerging framework of quantum utility and benchmarking, paving the way for exploring quantum advantage in condensed matter physics.

Wigner Localisation Simulated on Quantum Hardware

This study successfully modelled the energy landscape of a two-electron dimer on a six-site ring, representing a high-fidelity digital quantum simulation of Wigner localisation. By mapping the Coulomb interaction Hamiltonian onto a superconducting processor, researchers reconstructed the ground-state energy landscape across a range of interaction regimes, demonstrating the potential of quantum hardware to accurately simulate complex physical systems. The work rigorously benchmarks the IBM Heron 2 processor, translating established experimental models of electrons on liquid helium into the realm of modern quantum computing.

Achieving a relative error below 7% in the strong-interaction limit validates the platform’s capability to probe strongly correlated phases of matter. While the current model is classically verifiable, its significance lies in establishing a physical benchmark for the Heron 2 processor. The authors acknowledge limitations inherent in the six-qubit system, but propose a clear pathway towards investigating classically intractable phenomena on larger lattices, paving the way for future quantum simulations in condensed matter physics.