Quantum Computers’ Ability to Simulate Elusive Magnetic Behavior Could Challenge Classical Methods

Insider Brief

• A new study demonstrates that Quantinuum’s 56-qubit H2 quantum computer can simulate magnetic behavior that challenges classical methods, signaling practical progress toward quantum advantage in materials science.
• Researchers simulated Floquet prethermalization in a two-dimensional spin system, capturing equilibrium-like dynamics and extracting a diffusion constant from real-time quantum data using over 2,000 two-qubit gates.
• Classical benchmarking with state-of-the-art methods failed to reproduce the quantum results at comparable scale and timescales, suggesting that digital quantum simulations are entering a regime inaccessible to conventional techniques.

A new study demonstrates that a digital quantum computer can simulate magnetic behavior at scales and timescales that challenge the best classical methods, opening a path toward practical quantum advantage in materials science.

In a paper posted to the pre-print server arXiv, researchers at Quantinuum and collaborating institutions reported that their 56-qubit H2 quantum computer was able to simulate a form of magnetism known as Floquet prethermalization, a subtle effect where digital quantum systems temporarily behave like their continuous-time counterparts. The results mark one of the clearest demonstrations yet of digital quantum hardware outperforming classical simulations in a scientifically meaningful context.

The team used the H2 machine to model a grid of quantum spins — a stand-in for magnetic atoms — in a configuration known as the transverse-field Ising model. This system, though conceptually simple, quickly grows too complex for classical computers to simulate when it evolves over time, especially in two dimensions. The researchers found that their digital quantum simulation remained stable and physically meaningful on time and size scales that conventional methods cannot reliably reach.

“In addition to confirming the stability of dynamics subject to achievable digitization errors, we show direct evidence of local equilibration by computing diffusion constants associated with an emergent hydrodynamic description of the dynamics,” the authors write in the arXiv preprint, adding, “This work establishes digital quantum computers as powerful tools for studying continuous-time dynamics” in quantum systems.

Capturing Magnetic Dynamics

The study’s main achievement is capturing the dynamics of a quantum magnetic system that would typically heat up into randomness due to digitization errors. Instead, under the right conditions, the system settled into a long-lived, stable state — a phenomenon known as Floquet prethermalization.

Floquet prethermalization describes the temporary emergence of equilibrium behavior in periodically driven quantum systems. It occurs before inevitable heating drives the system toward disorder. One way to envision it: this is somewhat like the spinning a coin on a table — for a moment, it looks stable and balanced, but eventually it wobbles and falls. Floquet prethermalization is that fleeting moment of order before the chaos sets in.

The researchers used their digital quantum processor to simulate this phenomenon at circuit depths involving more than 2,000 two-qubit gates, something not previously achieved at this scale.

They further validated their findings by extracting a thermal transport coefficient—specifically, a diffusion constant—demonstrating that the simulated system obeyed the laws of hydrodynamics, a hallmark of equilibrium-like behavior in complex systems.

Long-Sought Goal

The ability to simulate real-time dynamics of quantum materials without uncontrolled approximations is one of the long-sought goals of quantum computing. While previous demonstrations of quantum advantage focused on synthetic, computationally hard tasks, this study targets a model with direct relevance to condensed matter physics.

The researchers write: “The utility of near-term quantum computers for simulating realistic quantum systems hinges on the stability of digital quantum matter — realized when discrete quantum gates approximate continuous time evolution — and whether it can be maintained at system sizes and time scales inaccessible to classical simulations.”

This raises the prospect that quantum computers could soon assist in studying strongly correlated systems, quantum thermalization, or emergent transport — areas central to understanding high-temperature superconductivity, quantum spin liquids, and other exotic phases of matter.

How Did They Do It?

The simulations involved evolving the transverse-field Ising model on a 7×8 rectangular lattice with periodic boundaries, using a second-order Trotter decomposition to approximate continuous-time evolution. To break that down a little more simply: this is a grid of 56 quantum spins arranged in a looped 7×8 pattern and the researchers relied on a technique called second-order Trotter decomposition to mimic continuous-time behavior with discrete quantum steps. The circuit used in each time step included native two-qubit gates (RZZ rotations) and single-qubit rotations, accumulating into thousands of gates over 20 time steps.

To assess the physical stability of the simulations, the researchers measured spin correlations and tracked their decay over time. They observed that if the Trotter step was too large, the system quickly heated to a trivial infinite-temperature state. However, for smaller steps, a prethermalized state emerged, retaining ordered magnetic domains over many steps.

To further test the results, they introduced an inhomogeneous initial state and watched as localized energy gradients relaxed over time — a behavior captured by a diffusion equation. From the decay of specific spatial modes, they extracted a diffusion constant of approximately 0.38, in line with expectations for thermal transport.

Classical Benchmarking

The team ran extensive comparisons using advanced classical methods including matrix product states (MPS), projected entangled pair states (PEPS), sparse Pauli dynamics, and neural network quantum states. Each method struggled with the full 7×8 system after only a few time steps, either due to memory limits, poor convergence, or uncontrollable truncation errors.

They write: “However, except in small systems, or at short times, the accuracy of these methods is difficult to assess, and it is a priori not clear when they can be trusted. While we have focused here on comparisons to classical methods using a practical amount of computational resources, the quantum simulations performed in this work remain reliable at timescales for which no classical methods we are aware of can be converged without extraordinary effort.”

While MPS methods performed well for low-entropy states, they broke down at intermediate temperatures due to exploding entanglement. PEPS methods showed promise but were limited by GPU memory. Neural network approaches failed to produce accurate results beyond early times for large lattices.

The authors applied zero-noise extrapolation (ZNE) techniques to remove hardware noise from quantum data, validating their approach by comparing results to classical methods in simpler cases.

Limitations and Future Work

The researchers are cautious not to declare full quantum supremacy, noting that future classical heuristics could still challenge or validate the results. They emphasize that their findings reflect the complementary strengths of quantum and classical approaches.

Still, the study suggests that digital quantum computers are reaching a threshold where they can model complex physical behavior that resists classical simulation—especially when combined with error mitigation strategies and careful algorithm design.

Looking forward, the team hopes to apply similar techniques to other models of interest in condensed matter and high-energy physics, and to develop quantum benchmarks that stress-test classical algorithms under realistic physical conditions.

This study marks a shift from synthetic benchmarks toward scientifically meaningful simulations. By demonstrating controlled prethermal behavior and extracting hydrodynamic properties from a programmable quantum computer, the research signals the growing maturity of quantum hardware.

“While we cannot predict the future capabilities of classical heuristics, a careful analysis of the limitations of numerous approximate methods indicates that the quantum data provided by H2 should be regarded as complementary to such heuristics, and is arguably the most convincing standard to which they should be compared,” the researchers write.

The work has not been officially peer reviewed. Scientists add their studies to pre-print servers, such as arXiv to receive faster feedback from their colleagues. However, peer review remains an important part of the scientific process.

The research involved contributors from multiple institutions across the globe. These include Quantinuum, with offices in Broomfield, Colorado; Munich, Germany; Cambridge, UK; and London, UK. Academic collaborators came from the Technical University of Munich and the Munich Center for Quantum Science and Technology in Germany; the California Institute of Technology, including its Division of Chemistry and Chemical Engineering, Division of Engineering and Applied Science, and the Institute for Quantum Information and Matter, in Pasadena, California; the Ecole Polytechnique Fédérale de Lausanne in Switzerland; and the University of Texas at Austin. Industry participation also included Fermioniq, based in Amsterdam, The Netherlands, and national laboratories such as Argonne National Laboratory and Oak Ridge National Laboratory in the United States.