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arXiv:2507.18079 · Communications Physics

Magnetic memory and hysteresis from quantum transitions in theory and experiments on quantum annealers

Frank P. Barrows, Elijah Pelofske, Pratik Sathe, Francesco Caravelli, Cristiano Nisoli

Published Sep 15, 2026• 0 citations
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Abstract

Abstract Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated protocols for robust hysteresis in large-scale transverse-field Ising systems on D-Wave quantum hardware. The quantum nature of these results remains to be understood, and existing theoretical approaches fail to capture the observed phenomenology in the far-from-equilibrium regime of driven longitudinal fields. Here, we present a hybrid framework that interleaves low-order Landau-Zener transitions with semiclassical domain wall kinetics, coupling the two channels through an iterative proportional fitting procedure that captures decoherence and measurement without requiring an explicit open-system model. Validated on three D-Wave annealers, the framework reproduces measured hysteresis loops, non-monotonic magnetization reversals, and transiently negative susceptibilities in rings of up to 4,906 qubits, and yields analytic scaling predictions for defect density and hysteresis area confirmed by experiment. These results establish programmable quantum annealers as platforms for exploring memory and non-equilibrium dynamics in driven quantum many-body systems.

DOI
10.1038/s42005-026-02847-6

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Abstract Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated protocols for robust hysteresis in large-scale transverse-field Ising systems on D-Wave quantum hardware. The quantum nature of these results remains to be understood, and existing theoretical approaches fail to capture the observed phenomenology in the far-from-equilibrium regime of driven longitudinal fields. Here, we present a hybrid framework that interleaves low-order Landau-Zener transitions with semiclassical domain wall kinetics, coupling the two channels through an iterative proportional fitting procedure that captures decoherence and measurement without requiring an explicit open-system model. Validated on three D-Wave annealers, the framework reproduces measured hysteresis loops, non-monotonic magnetization reversals, and transiently negative susceptibilities in rings of up to 4,906 qubits, and yields analytic scaling predictions for defect density and hysteresis area confirmed by experiment. These results establish programmable quantum annealers as platforms for exploring memory and non-equilibrium dynamics in driven quantum many-body systems.
While quantum annealers have emerged as versatile and controllable platforms for experimenting on correlated spin systems, the important phenomenology of magnetic memory and hysteresis remain unexplored on hardware designed to escape metastable states via quantum tunneling. Here, we present the first general protocol to experiment on magnetic hysteresis on programmable quantum annealers and implement it on three D-Wave superconducting qubit quantum annealers, using up to thousands of spins, for both ferromagnetic and disordered Ising models, and across different graph topologies. We observe hysteresis loops whose area depends nonmonotonically on quantum fluctuations, exhibiting both expected and unexpected features, such as disorder-induced steps and nonmonotonicities. Our work establishes quantum annealers as a platform for probing nonequilibrium emergent magnetic phenomena, thereby broadening the role of analog quantum computers into foundational questions in condensed matter physics.
Using programmable analog quantum annealing processors, we implement a sampling-based magnetic hysteresis protocol to probe the counterintuitive notion of magnetic memory in antiferromagnetic models. A key component of this protocol responsible for the hysteresis is a transverse field, which enables state transitions, while the longitudinal magnetic field sweep is done via a longitudinal control field. We observe intriguing non-monotonic magnetization, alongside full saturation and reversal of the hysteresis curve, Barkhausen-like noise, as well as emergent magnetic domains mediated by quantum fluctuations that give rise to the magnetic memory effect in antiferromagnets.
Quantum annealers can provide non-local optimization by tunneling between states in a process that ideally eliminates memory of the initial configuration. We study the crossover between memory loss and retention due to quantum fluctuations, in a transverse Ising model on odd numbered antiferromagnetic rings of thousands of spins with periodic boundary conditions, by performing reverse quantum annealing experiments on three programmable superconducting flux qubit quantum annealers. After initializing the spins to contain a single domain wall, we then expose it to quantum fluctuations by turning on the transverse Zeeman energy. We characterize the crossover between memory retention at low transverse field, and memory loss at high transverse field by extracting the Shannon information entropy of magnetic domain wall distributions. We demonstrate a clear crossover in memory retention, and its dependence on hardware platform and simulation time. Our approach establishes a general probe of the interplay between quantum fluctuations and memory.
Recently, a Hamiltonian dynamics simulation was performed on a kicked ferromagnetic 2D transverse field Ising model with a connectivity graph native to the 127 qubit heavy-hex IBM Quantum architecture using ZNE quantum error mitigation. We demonstrate that one of the observables in this Trotterized Hamiltonian dynamics simulation, namely magnetization, can be efficiently simulated on current superconducting qubit-based programmable quantum annealing computers. We show this using two distinct methods: reverse quantum annealing and h-gain state encoding. This simulation is possible because the 127 qubit heavy-hex connectivity graph can be natively embedded onto the D-Wave Pegasus quantum annealer hardware graph and because there exists a direct equivalence between the energy scales of the two types of quantum computers. We derive equivalent anneal pauses in order to simulate the Trotterized quantum circuit dynamics for varying Rx rotations θh∈(0,π2]θ_h \in (0, \fracπ{2}]θh​∈(0,2π​], using quantum annealing processors. Multiple disjoint instances of the Ising model of interest can be embedded onto the D-Wave Pegasus hardware graph, allowing for parallel quantum annealing. We report equivalent magnetization dynamics using quantum annealing for time steps of 20, 50 up to 10,000, which we find are consistent with exact classical 27 qubit heavy-hex Trotterized circuit magnetization dynamics, and we observe reasonable, albeit noisy, agreement with the existing simulations for single site magnetization at 20 Trotter steps. The quantum annealers are able to simulate equivalent magnetization dynamics for thousands of time steps, significantly out of the computational reach of the digital quantum computers on which the original Hamiltonian dynamics simulations were performed.
Geometrically frustrated spin-chain compounds such as Ca 3 Co 2 O 6 exhibit extremely slow relaxation under a changing magnetic field.Consequently, both low-temperature laboratory experiments and Monte Carlo simulations have shown peculiar out-of-equilibrium magnetization curves, which arise from trapping in metastable configurations.In this work, we simulate this phenomenon in a superconducting quantum annealing processor, allowing us to probe the impact of quantum fluctuations on both the equilibrium and dynamics of the system.Increasing the quantum fluctuations with a transverse field reduces the impact of metastable traps in out-of-equilibrium samples and aids the development of three-sublattice ferrimagnetic (up-up-down) long-range order with magnetization 1/3.At equilibrium, we identify a finitetemperature shoulder in the 1/3-to-saturated phase transition, promoted by quantum fluctuations but with an entropic origin.This work demonstrates the viability of dynamical as well as equilibrium studies of frustrated magnetism using large-scale programmable quantum systems and is therefore an important step toward programmable simulation of dynamics in materials using quantum hardware.
We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of the XY (or effectively Ising) model in a transverse field. Then, we obtain the mean-field estimate for the equilibrium gap in the ground-state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau’s (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes’ (1963) decomposition of the mean field into the orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each of the component following Suzuki–Kubo (1968) mean-field dynamics. Next, we discuss its applications to quantum hysteresis in Ising magnets (in the presence of an oscillating transverse field), to quantum heat engines (employing the transverse Ising model as a working fluid), and to the quantum annealing of the Sherrington–Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides us with a very fast computational algorithm, leading to ground-state energy values converging to the best-known analytic estimate for the model. Finally, we summarize the main results obtained and draw conclusions about the effectiveness of the de Gennes–Suzuki–Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems.