Quantum Simulation Models Magnetism in Materials Using up to 48 Qubits

A quantum simulation of magnetic materials, specifically chromium tri-halide monolayers, has been achieved by Pascal Stadler and colleagues at HQS Quantum Simulations GmbH, reaching systems with up to 48 qubits. The simulation validates quantum results against classical benchmarks and demonstrates the growing possibility of modelling real materials using commercial quantum computing platforms, even without immediate quantum advantage over existing methods. The team’s simulation of low-energy magnetic excitations, or spin-wave spectra, represents a key step towards using quantum computation for materials science.

Quantum simulation extends magnetic modelling to unprecedented system sizes

The quantum simulation agreed with classical benchmarks for up to 48 spins, exceeding the 24-spin limit of prior Krylov-based simulations and matching the capacity of density matrix renormalization group calculations. Simulating materials with this many interacting spins demands exponentially increasing computational resources on conventional machines, a consequence of the inherent complexity of many-body quantum systems. Classical methods, while powerful, struggle to accurately represent the quantum states of these systems as the number of interacting particles increases. Krylov subspace methods, a common approach for approximating quantum dynamics, become computationally prohibitive beyond a certain system size, typically around 24 spins in this context. Density matrix renormalization group (DMRG) techniques, while more efficient for one-dimensional or quasi-one-dimensional systems, also face limitations when applied to larger two-dimensional materials. Researchers at IQM Resonance and their colleagues successfully modelled low-energy magnetic excitations, or spin-wave spectra, in chromium tri-halide monolayers using a cloud-based quantum computer.

This unlocks the modelling of larger, more complex magnetic systems previously intractable for classical computers. Chromium tri-halide monolayers, two-dimensional materials exhibiting magnetism, were the focus of the team, and an effective spin model was derived from initial ab-initio electronic structure calculations. These calculations, based on density functional theory (DFT), determine the electronic structure of the material, including the interactions between electrons and their influence on the magnetic moments of the atoms. The effective spin model simplifies the complex electronic interactions into a more manageable representation of the magnetic behaviour, focusing on the interactions between the spins of the atoms. This model represents the magnetic interactions within the material, typically described by parameters like the exchange coupling constants. The simulation exhibited quasi-constant wall-time scaling, a strong advantage over the exponential scaling inherent in classical methods, suggesting a pathway towards efficient modelling of magnetic materials with quantum computation. This quasi-constant scaling implies that the time required to perform the simulation increases linearly with system size, rather than exponentially, offering a significant potential speedup for larger systems.

Focusing on high-symmetry wave vectors, Γ, K and M, simulations were performed on IQM Resonance’s Garnet and Emerald chips to analyse magnon dispersion relations, which can be experimentally verified using inelastic neutron scattering. Magnons are quantized spin waves, and their dispersion relation describes the relationship between their energy and momentum. Inelastic neutron scattering is a technique used to probe these magnons and experimentally determine the magnon dispersion relation, providing a direct comparison with the simulation results. The choice of high-symmetry wave vectors simplifies the analysis and allows for a more focused comparison with experimental data. Despite challenges remaining in resolving certain spectral features on current Noisy Intermediate-Scale Quantum (NISQ) devices, the workflow demonstrates the potential for domain experts to utilise cloud-based quantum computers for materials science. NISQ devices are prone to errors due to limitations in qubit coherence and gate fidelity, which can affect the accuracy of the simulation results. These errors manifest as noise in the spectra, making it difficult to resolve finer details.

Accurately modelling even simple magnetic systems has long strained the limits of classical computing, yet simulating materials at the atomic level promises breakthroughs in fields from energy storage to medicine. Understanding the magnetic properties of materials is crucial for developing new technologies in areas such as magnetic data storage, spintronics, and magnetic resonance imaging. The ability to accurately simulate these properties can accelerate the discovery and design of new materials with tailored magnetic characteristics. The simulation of chromium tri-halide is a significant step towards this goal, providing a platform for exploring more complex magnetic materials and phenomena. The authors openly acknowledge that resolving finer details within these spectra currently proves difficult with today’s noisy intermediate-scale quantum (NISQ) devices; further refinement of both hardware and algorithms will be necessary to fully realise the potential of this approach. Improvements in qubit coherence times, gate fidelities, and error correction techniques are essential for overcoming the limitations of current NISQ devices. Furthermore, the development of more efficient quantum algorithms tailored to materials science applications will be crucial for maximising the benefits of quantum computation.

Spin-wave spectra, or magnons, represent collective magnetic excitations within materials, and their accurate modelling is vital for understanding material properties. These excitations play a crucial role in determining the thermal and magnetic properties of materials, influencing their behaviour at finite temperatures. The feasibility of utilising commercial quantum platforms for materials science is demonstrated, offering domain experts early access to potentially major computational tools. This accessibility is particularly important for researchers who may not have the resources to develop and maintain their own quantum computing infrastructure. The current limitations of quantum hardware do not invalidate the progress made, but rather highlight areas for future development. The validation against classical benchmarks provides confidence in the accuracy of the quantum simulation, even with the limitations of current hardware.

This simulation of chromium tri-halide’s magnetic behaviour demonstrates the growing potential of cloud-based quantum computing for materials science. Allowing for the investigation of more complex systems than previously possible, agreement with benchmarks using up to 48 qubits signifies a key step. The observed quasi-constant wall-time scaling offers a potential advantage, hinting at future efficiency gains as quantum hardware matures and algorithms are optimised. As quantum computers continue to improve in terms of qubit count, coherence, and fidelity, the scope of materials that can be accurately simulated will expand, paving the way for new discoveries and innovations in materials science and beyond. The ability to efficiently model these materials will be crucial for addressing some of the most pressing challenges facing society, from developing sustainable energy sources to creating advanced medical technologies.

The research successfully simulated low-energy magnetic excitations in chromium tri-halide monolayers using up to 48 qubits on a commercial quantum computer. This demonstrates that useful quantum simulations of real materials are now achievable for researchers with access to cloud-based quantum computing platforms. Although current quantum devices have limitations, the simulation achieved good agreement with classical benchmarks and exhibited a potentially more efficient scaling behaviour. The authors suggest continued development of these methods will be crucial for maximising the benefits of quantum computation in materials science.