Researchers at Los Alamos National Laboratory have observed full saturation and reversal of the hysteresis curve in antiferromagnetic models using programmable quantum annealers. This finding challenges expectations, as antiferromagnets typically resist magnetization, making complete reversal an unusual result. The team detected Barkhausen-like noise, typically associated with ferromagnetic materials, alongside emergent magnetic domains created by quantum fluctuations. These fluctuations mediate magnetic memory within the antiferromagnets, demonstrating a direct link between quantum effects and a material property.
Programmable Quantum Annealers Probe Antiferromagnetic Hysteresis
The team implemented a sampling-based magnetic hysteresis protocol on these processors to investigate magnetic memory within antiferromagnetic models, revealing unexpected results about how these materials respond to external fields. This approach allows for emulation of magnetic hysteresis experiments, offering a new avenue for studying complex magnetic phenomena.
The Los Alamos team focused on Transverse-Field Ising Models, both one and two-dimensional, as baseline geometries for probing antiferromagnetic hysteresis, and also examined results from D-Wave processor lattices with more complex connectivity. These quantum annealers operate at approximately 15 millikelvin, using superconducting flux qubits connected in repeating subgraph units, and are programmed to realize time-dependent transverse field Ising models.
The researchers’ protocol uses a transverse field to enable state transitions, while a longitudinal control field performs magnetic field sweeps, allowing for detailed observation of the antiferromagnetic response. “While originally designed to solve optimization problems, quantum annealers are also emerging as programmable laboratories for physical phenomena,” explained the researchers in their report. Examining domain wall statistics and individual measurements revealed fragmented antiferromagnetic ordering in the approximately de-polarized region of the hysteresis cycles, indicating a complex internal structure.
Further analysis of the 2D antiferromagnetic square lattices, conducted on four different D-Wave quantum annealers, showed average magnetization as a function of the applied longitudinal field. Overlaid black arrows on the average magnetization lines denote the time-progression of the analog simulations, as well as the direction of the longitudinal field sweeps, providing a visual representation of the dynamic magnetic behavior.
The study also considered models exhibiting frustration, mirroring the behavior of real magnetic compounds with quasi-one-dimensional or triangular 2-dimensional lattices. The researchers expanded the range of phenomena accessible through these experiments, moving beyond bulk material observables and classical simulation techniques. This work opens the door to exploring magnetic properties in previously inaccessible regimes, potentially leading to new insights into the fundamental behavior of antiferromagnetic materials and their potential applications. The ability to program and probe these systems with quantum annealers represents an advancement in the field of magnetism.
Transverse Fields Enable State Transitions in Antiferromagnets
The application of a transverse field allows for complete polarization of antiferromagnets, a result achieved through a sampling-based magnetic hysteresis protocol implemented on programmable quantum annealing processors. This contrasts with typical antiferromagnetic behavior, where complete magnetization reversal is not expected due to the inherent resistance to alignment of opposing magnetic moments. The observed full saturation and reversal occurred even in antiferromagnetic lattices where full magnetization is not normally reached, demonstrating a novel ability to manipulate these systems.
Simulations revealed that the ratio between the transverse field strength (Γ) and lattice coupling (J) is critical for observing hysteresis. A field too weak fails to induce state transitions, while a sufficiently strong coupling is necessary to measure the effect. The simulations detected Barkhausen-like steps in the magnetization cycles, a phenomenon traditionally associated with ferromagnetic materials, suggesting a more complex interplay of magnetic domains than previously understood.
The emergence of these magnetic domains is directly linked to quantum fluctuations, demonstrating that quantum effects are not merely theoretical but actively mediate the magnetic memory effect within the antiferromagnets. These fluctuations enable transitions between states, even in the absence of classical metastability, and allow for the observation of minor-loop hysteresis curves resembling those seen in ferromagnetic materials. The use of statistics-balancing calibration on the quantum hardware further improved the quality of these simulations, particularly on full-hardware-graph antiferromagnets.
The researchers found that for low-coordination antiferromagnets, such as one- and two-dimensional Ising models, an appropriately tuned ratio of transverse field to lattice coupling can achieve full polarization. This is significant because the ground state subspace of these systems contains an odd number of domain walls, and local spin flips typically conserve the parity of the domain wall count.
The ability to overcome this constraint and achieve full polarization highlights the power of the transverse field in driving state transitions and manipulating the magnetic order. “Because N is odd, there are an odd number of domain walls for any computational basis ( basis) configuration,” the study notes, explaining the initial conditions overcome by the transverse field. The protocol’s reliance on sampling and probabilistic measurements offers a unique approach to studying hysteresis, allowing for the observation of subtle effects that might be missed in traditional experiments.
D-Wave QPUs Simulate Magnetic Hysteresis Protocols
Simulations using D-Wave quantum processing units reveal a surprising level of control over antiferromagnetic materials, demonstrating the formation of magnetic domains and full reversal of magnetic hysteresis even in systems designed to resist magnetization. Experiments across four different D-Wave QPUs, each with either Pegasus or Zephyr connectivity, showed consistent qualitative behavior in the simulated antiferromagnetic response, despite variations in device settings and physical parameters.
Researchers extracted both spin structure factor and the antiferromagnetic order parameter to monitor magnetic order throughout the hysteresis cycles, providing detailed insight into the behavior of these complex systems. Analysis of one-dimensional antiferromagnetic rings revealed fragmented antiferromagnetic ordering during the de-polarized regions of the hysteresis cycles, with domain wall density mirroring the magnetization, though reversed in sign to account for the D-Wave processor Hamiltonian.
These domain wall measurements, qualitatively similar across the tested QPUs, suggest a potential use for these systems as probes of defect transport within the antiferromagnetic material. “We find several interesting phenomena, including non-monotonicities similar to those observed in low-dimensional ferromagnetic models,” the researchers report, highlighting the unexpected parallels between traditionally opposing magnetic behaviors. These experiments build on previous work applying the method to ferromagnetic and disordered Ising models, extending the range of accessible phenomena and probing counterintuitive magnetic behavior.
The ability to observe full saturation and reversal is particularly noteworthy, given the inherent resistance to magnetization characteristic of antiferromagnets, and suggests a new level of control over these materials using quantum annealing technology. The researchers’ approach relies on sampling and probabilistic measurements, offering a unique pathway to study hysteresis and related magnetic phenomena in regimes previously inaccessible to classical simulation.
Non-Monotonic Magnetization Reveals Antiferromagnetic Behavior
Experiments with quantum annealers have revealed unexpected behavior in antiferromagnetic materials, specifically non-monotonic magnetization curves during hysteresis measurements. Analysis of domain walls, boundaries between regions of differing magnetic alignment, showed fragmented antiferromagnetic ordering within the partially demagnetized regions of the hysteresis cycles. This fragmentation suggests that the process of reversing magnetization in these materials isn’t uniform, but occurs through the formation and movement of these localized magnetic domains.
The team extracted the spin structure factor to monitor magnetic transitions during the hysteresis cycles, confirming a clear shift from ferromagnetic-like ordering when fully polarized to a more complex antiferromagnetic state. These 2-dimensional experiments demonstrated that the models could be fully saturated when the ratio of transverse to longitudinal coupling was appropriately tuned and the longitudinal field was sufficiently strong.
The observed magnetic behavior is linked to a competition between exchange energy, the energy arising from interactions between electron spins, and the applied longitudinal field. For antiferromagnetic rings with an odd number of domain walls, the longitudinal field term contributes differently depending on the wall’s orientation, creating a unique energy landscape. This landscape, the researchers found, leads to an avoided crossing and underlies the “stick-slip” dynamics and step-like magnetization changes characteristic of the antiferromagnetic hysteresis.
The work demonstrates large-scale simulations of antiferromagnetic hysteresis using quantum computers for the first time, and the results show clear transitions of magnetic ordering during the hysteresis cycles. The structure factor plots reveal a clear antiferromagnetic ordering transition from ferromagnetic-like ordering when the systems are fully polarized, as well as boundary effects.
Extracting Néel Order Parameter from Hysteresis Cycles
Extracting the Néel order parameter from hysteresis cycles proved possible through simulations performed on four distinct D-Wave quantum annealing quantum processing units (QPUs), revealing unexpected magnetic behavior in antiferromagnetic models. Analysis of the simulations revealed the formation of magnetic domains as expected with increasing longitudinal field strength, alongside a quantifiable measure of domain wall density. This domain wall density, observed across three of the QPUs, showed qualitative similarities, with data available in supplementary information.
To further investigate these experiments, the team considered the transverse-field Ising antiferromagnet on a ring, defined by a specific Hamiltonian, allowing for a detailed examination of the interplay between exchange energy and external fields. The simulations revealed Barkhausen-like noise, abrupt, jerky changes in magnetization, in regimes where the system was fully polarized, a phenomenon typically associated with ferromagnetic materials. The researchers report, highlighting the unexpected appearance of this behavior in an antiferromagnetic context.
The study’s computational capability, using near-term analog quantum computers, offers a unique advantage in examining phenomena difficult to systematically study in traditional magnetic laboratories. Future work will focus on calibrated antiferromagnetic hysteresis cycle simulations, particularly on two-dimensional systems where statistical fluctuations in the antiferromagnetic order parameter are larger, and on refining the accuracy of coupler and flux bias offsets. This research highlights the potential of programmable quantum annealers to reveal new insights into complex magnetic phenomena and advance the understanding of magnetic memory effects in antiferromagnets.
Quantum Fluctuations Drive Magnetic Memory Effects
Boundary effects were also apparent in these structure factor plots, adding another layer of detail to the observed magnetic behavior. “This computational capability of near term analog quantum computers highlights that the full programmability of these devices inherently gives us the capability to examine phenomena which are hard to systematically study in magnetic laboratories,” the researchers report.
TFIM Models as Baseline for Antiferromagnetic Studies
The ability to embed one-dimensional antiferromagnetic models onto D-Wave processors enabled simulations of up to 4905 qubits on the , demonstrating a significant scaling capability for these quantum annealing platforms. Researchers used the Glasgow solver, a graph isomorphism finder within the minorminer package, to map these models onto the hardware graph, a step in translating theoretical constructs into physical experiments. This embedding process, while successful, revealed limitations; the maximum system sizes varied across different D-Wave architectures, with the supporting only 1131 qubits for the 1D model.
The choice of coupler values, consistently set to 1, the maximum allowable strength, highlights a deliberate effort to maximize interaction within the simulated systems. While the 2D square-grid antiferromagnetic model, with its open boundary conditions, represents an unfrustrated magnetic system, the pseudo-3D model introduces magnetic frustration due to its non-bipartite nature.
This deliberate inclusion of frustration, alongside the 1D system’s inherent frustration from having an odd number of spins, allows for a comparative study of how these factors influence magnetic behavior. The team collected data from 2,000 measurements for the 1D model and 8,000 measurements for the quasi-3D model per data point, ensuring statistical robustness in their findings. These simulations, built upon Transverse-Field Ising Models, provide a baseline for understanding antiferromagnetic hysteresis, a phenomenon where the material’s magnetization lags behind the applied field.
The choice of TFIM as a foundational model is strategic, allowing researchers to systematically probe the interplay between quantum fluctuations and magnetic ordering. The implementation of a sampling-based magnetic hysteresis protocol on programmable analog quantum annealers represents a novel approach to studying these complex systems, offering a pathway to explore regimes previously inaccessible to classical computation.
👉 More information
🗞 Probing antiferromagnetic hysteresis on programmable quantum annealers
✍️ Elijah Pelofske, Pratik Sathe, Cristiano Nisoli and Frank Barrows
🧠 DOI: http://link.aps.org/doi/10.1103/mcz4-xh6z
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