D-Wave Quantum Annealers With Landau-Zener Transitions
Landau-Zener Transitions and Domain-Wall Kinetics Explain Quantum Annealer Hysteresis Quantum annealers, which aim to solve difficult problems efficiently, are thought to avoid persistent memory effects seen in conventional computational methods. However, recent experiments have revealed real hysteresis in these quantum systems, a surprising result. This discovery challenges the current understanding of memory creation in physical systems and opens up new avenues for quantum computing research.
Unexpected Memory Effect in Quantum Systems
Hysteresis occurs when a material's reaction, such as magnetisation, lags after the applied external field, demonstrating a form of memory based on earlier exposure. Despite using quantum tunnelling, quantum annealers show magnetisation lagging behind an applied field.
Scientists from Q-MAFIA at Los Alamos National Laboratory, including Frank Barrows, Elijah Pelofske, and Pratik Sathe, and Francesco Caravelli from the Universit~a di Pisa and Scuola Normale Superiore, developed a theoretical framework to explain this unusual behaviour. Their key research indicates that this substantial hysteresis is caused by the complicated interaction between discrete quantum transitions and the continual domain wall movement inside the annealer. In essence, this interaction provides quantum system memory.
Connecting Quantum and Classical Dynamics
The researchers use quantum and conventional physics to explain the observed behaviours. The model incorporates semiclassical domain-wall kinetics and Landau-Zener transitions. Landau-Zener transitions govern system evolution's discrete quantum transitions. Connecting these underlying quantum processes with domain border movement allowed researchers to mimic complex hysteretic activity in investigations. Quantum annealers may imitate and repeat observable behaviour, making them useful for studying programmable quantum hysteresis. This theoretical approach's main strength is its ability to replicate experimental data from numerous annealers and model quantum system behaviour. Importantly, the model helps researchers identify memory effects like temporary negative susceptibilities. This identification proves the annealers are documenting their former status.
Experimental D-Wave Annealers Validation
The study employed D-Wave quantum annealers to simulate magnetic hysteresis in depth to validate their approach. These studies used a quantum annealer with 4,906 qubits to test the model. The ubiquitous Ising model explained the spin-interacting systems under study. An external magnetic field was used to measure the systems' response. On D-Wave quantum annealers, hundreds of qubits were carefully used to form two-dimensional lattices and one-dimensional magnetic chains. Extremely reproducible hysteretic loops were found after carefully adjusting the applied field and measuring the magnetisation. Loops were observed in classical physics contexts where memory effects would not be expected. The simulation findings show that the system's dimensionality and, most crucially, annealing length affect simulation quality. Researchers evaluated how annealing time—the time the D-Wave machine spends finding the lowest energy state—affected results across short and long durations. Two-dimensional simulations yielded smoother and more stable hysteresis loops than one-dimensional simulations, which were more unexpected. The study highlighted how low-dimensional systems' increased noise sensitivity makes simulation harder. Longer annealing times created smoother loops with smaller areas, according to simulations. This makes sense because more time helps the system reach its lowest energy state. The researchers accurately mapped the problem configuration onto D-Wave circuitry using antiferromagnetic gauge transformations. These adjustments made transferring the Ising model to quantum annealing technology practical and efficient.
Relevance and Future Plans
The developed framework accurately predicted how the hysteresis loop will change as the applied field speed varies and replicated complex hysteretic behaviour, including non-monotonic magnetisation reversals and observed variations in the loop's area. The model also replicates local entanglement signs. These findings suggest that programmable annealers are ideal for studying complex, non-equilibrium dynamics in many-body systems. The study establishes these devices as powerful experimental platforms for studying complex quantum phenomena by confirming memory effects. They enable memory-behaving system research. D-Wave quantum annealers can study more complex magnetic systems, which may help us understand magnetism. This study has improved our understanding of quantum memory and its potential uses in quantum technology.