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arXiv:2509.10927

Erasing Classical Memory with Quantum Fluctuations: Shannon Information Entropy of Reverse Quantum Annealing

Elijah Pelofske, Cristiano Nisoli

Published Sep 13, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2509.10927

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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.
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.
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.
Abstract Metastable domain-wall networks in correlated materials can relax on timescales vastly longer than the microscopic processes that move their elementary constituents. Motivated by the slow domain-wall rearrangements observed in 1T-TaS 2_22​ , we study a phenomenological spin model designed to isolate the interplay between local domain-wall hopping and environmental noise. The model contains discrete registry-like configurations, energetic costs for domain walls, and a transverse-field-induced hopping channel, and is implemented on a superconducting quantum annealer with more than 2000 logical degrees of freedom. A Schrieffer–Wolff analysis shows that the intrinsic hopping amplitude arises at second order in the transverse field and is therefore fast on device timescales. However, the measured reconfiguration rate saturates to a finite value at low effective temperature and depends only weakly on the hopping amplitude. This indicates that domain-wall motion is not limited by bare tunnelling, but by quasi-static longitudinal-field noise that detunes neighboring configurations and intermittently permits local hopping events. These results demonstrate how noise can slow domain-wall motion in a minimal quantum-simulation model and suggest a possible mechanism for ultra-slow relaxation in charge-ordered materials.
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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.
A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterising the annealer. The noise measured in this fashion is smaller than what is seen during the single-qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.