Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers

For nearly a century, scientists have used a simple test to understand how materials remember their past. By applying a magnetic field to a piece of iron and then slowly reversing it, they observe a lag: the material does not immediately flip its magnetic direction when the external force changes. Instead, it resists, holding onto its original orientation until the opposing force becomes strong enough to break its grip. This phenomenon, known as hysteresis, is the reason magnets can store data and why certain materials act as memory devices. In the classical world of everyday physics, this behavior is well understood and relies on the existence of stable magnetic regions that resist change. However, a fundamental rule of classical physics states that in a one-dimensional line of magnetic atoms, such resistance should be impossible. Without the extra dimension to create complex, stable structures, these lines should flip instantly and perfectly with the applied field, showing no memory at all.

This creates a puzzling situation for modern physics. Researchers have recently begun using powerful quantum computers, specifically devices designed to solve complex optimization problems, to simulate magnetic materials. These machines operate at temperatures near absolute zero and use the strange rules of quantum mechanics, where particles can exist in multiple states at once and tunnel through barriers. Because these quantum systems are designed to escape stuck states and find the best solution quickly, they were expected to eliminate the very memory effects that cause hysteresis. Yet, when scientists ran experiments on these machines, they found the opposite. Even in one-dimensional lines of thousands of quantum bits, the system refused to flip instantly. It displayed a stubborn resistance, a clear memory of its previous state, and a lag that defied classical expectations. This discovery suggests that quantum mechanics, rather than erasing memory, can create entirely new kinds of it.

In a new study, a team of researchers at Los Alamos National Laboratory set out to understand this surprising behavior. They used three different generations of D-Wave quantum annealers, which are specialized computers containing thousands of superconducting qubits. The researchers programmed these machines to act as long rings of magnetic spins, some containing as many as 4,906 individual units. They then applied a magnetic field that slowly changed direction, mimicking the classic hysteresis test. The results were striking. Even in the one-dimensional rings, where classical physics predicts no resistance, the quantum system showed a distinct "coercivity," a measure of how hard it is to flip the magnetization. The system did not just flip; it hesitated, creating a loop in the data that proved it was remembering its past orientation. This memory persisted even in regimes where classical theory says it should be forbidden.

To explain how this happens, the team developed a new theoretical framework that combines two different ways of looking at the problem. They realized that the system behaves like a hybrid of a quantum machine and a classical one. On the quantum side, the system undergoes rapid, discrete jumps between energy states, similar to a particle tunneling through a wall. On the classical side, once these jumps occur, the system behaves like a collection of moving boundaries, or "domain walls," that separate regions of different magnetic alignment. The researchers found that the memory effect arises from the interplay between these two processes. The quantum jumps create excited states that are not the lowest energy configuration, and the movement of the domain walls determines how quickly the system can relax back to a stable state. Because the system gets trapped in these excited states for a while, it cannot flip instantly, creating the observed lag.

The study confirmed that this behavior is not just a glitch of the hardware but a genuine physical phenomenon. The researchers observed specific signatures that only a quantum system could produce, such as a temporary negative response to the magnetic field and non-monotonic reversals, where the magnetization flips back and forth in a complex pattern before settling. These features were reproduced in their computer simulations, which used a method that alternates between calculating exact quantum transitions and modeling the movement of magnetic boundaries. The simulations matched the experimental data from the quantum annealers almost perfectly, capturing the shape of the hysteresis loops and the way the memory effect changed as the speed of the field sweep was altered.

One of the most significant findings is that this quantum memory is distinct from the thermal memory seen in ordinary materials. In a standard magnet, heat helps the material flip. In these quantum experiments, the memory persists even when the system is cold enough that thermal fluctuations are negligible. Instead, the memory is driven by the competition between the speed at which the magnetic field is changed and the natural energy gaps between the quantum states. If the field is changed too quickly, the system cannot keep up and gets stuck in a high-energy state. If it is changed slowly, the system has time to relax. The researchers found that by tuning the strength of the quantum forces and the speed of the sweep, they could control the size of the memory effect, shrinking or expanding the hysteresis loop at will.

The team also explored how the size of the system affects this behavior. They tested rings ranging from just four qubits to nearly five thousand. In the smallest systems, the quantum effects were most pronounced, but the memory effect remained robust even in the largest rings. This suggests that the phenomenon is not a small-scale anomaly but a fundamental property of how quantum systems evolve when driven out of equilibrium. The researchers noted that in two-dimensional grids, the behavior was different, with stronger magnetic ordering and larger fields required to flip the spins, consistent with what is known about classical magnets. However, the one-dimensional rings remained the most surprising, as they exhibited a level of resistance that classical physics says should not exist.

This work establishes quantum annealers as powerful tools for studying non-equilibrium dynamics, a field that deals with how systems behave when they are being pushed and pulled rather than sitting in a calm state. By demonstrating that these machines can exhibit programmable memory, the researchers have opened a new avenue for exploring how quantum systems process information and retain history. The ability to observe and control these effects in a programmable device means that scientists can now test theories about quantum memory and phase transitions in a way that was previously impossible. The study does not claim to have solved all the mysteries of quantum magnetism, but it provides a clear, experimentally verified picture of how memory can emerge from the chaotic dance of quantum transitions and domain wall motion.

The implications of these findings extend beyond the specific machines used in the experiment. The hybrid model developed by the researchers, which mixes quantum calculations with classical descriptions of moving boundaries, offers a new way to simulate complex magnetic materials. This approach could help scientists design better magnetic storage devices or understand the behavior of exotic materials that do not fit into standard categories. More importantly, it highlights that quantum computers are not just faster calculators; they are unique laboratories where the fundamental laws of physics can be tested and manipulated. The observation of hysteresis in a one-dimensional quantum system serves as a reminder that nature often holds surprises that challenge our most basic assumptions, and that the boundary between the quantum and classical worlds is far more porous than previously thought.

The researchers concluded that the memory observed in these experiments is a genuine quantum effect, arising from the specific way the system transitions between states and relaxes. They ruled out the possibility that the results were simply due to heat or classical noise, as the behavior persisted under conditions where those factors should have been negligible. Instead, the memory is a direct result of the system's inability to instantly adapt to the changing magnetic field, a lag created by the finite time it takes for quantum transitions to occur and for the resulting magnetic domains to rearrange. This work provides a concrete example of how quantum mechanics can give rise to collective behaviors that mimic, and in some cases exceed, the capabilities of classical materials. It suggests that by understanding and harnessing these quantum memory effects, we may be able to develop new types of computing and sensing technologies that operate on principles we are only beginning to understand.