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Scientific Reports

Quantum simulation of noise-slowed domain-wall motion in a phenomenological spin model

Jaka Vodeb

Published Jul 23, 2026• 0 citations
Publisher

Abstract

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 $$_2$$ , 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.

DOI
10.1038/s41598-026-63377-3

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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.
Relaxation dynamics of complex many-body quantum systems brought out of equilibrium and subsequently trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and new energy-efficient memory devices. Understanding the dynamics of such systems is crucial for exploring fundamental aspects of many-body non-equilibrium quantum physics. In this work we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material where classical dynamics is topologically constrained. The crossover from temperature to quantum fluctuation dominated dynamics in the context of environmental noise is investigated by directly observing charge reconfiguration with time-resolved scanning tunneling microscopy. The process is modelled using a programmable superconducting quantum simulator in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment on the quantum material and the simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics remarkably well. The combined experiment and simulations lead to a better understanding of noise-driven quantum dynamics in open quantum systems. From a practical viewpoint, the results are important for understanding the origin of the retention time in non-volatile memory devices such as those based on 1T-TaS2.
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.
Domains are homogeneous areas of discrete symmetry, created in nonequilibrium phase transitions. They are separated by domain walls, topological objects which prevent them from fusing together. Domains may reconfigure by thermally-driven microscopic processes, and in quantum systems, by macroscopic quantum tunnelling. The underlying microscopic physics that defines the system's energy landscape for tunnelling is of interest in many different systems, from cosmology and other quantum domain systems, and more generally to nuclear physics, matter waves, magnetism, and biology. A unique opportunity to investigate the dynamics of microscopic correlations leading to emergent behaviour, such as quantum domain dynamics is offered by quantum materials. Here, as a direct realization of Feynman's idea of using a quantum computer to simulate a quantum system, we report an investigation of quantum electron reconfiguration dynamics and domain melting in two matching embodiments: a prototypical two-dimensionally electronically ordered solid-state quantum material and a simulation on a latest-generation quantum simulator. We use scanning tunnelling microscopy to measure the time-evolution of electronic domain reconfiguration dynamics and compare this with the time evolution of domains in an ensemble of entangled correlated electrons in simulated quantum domain melting. The domain reconfiguration is found to proceed by tunnelling in an emergent, self-configuring energy landscape, with characteristic step-like time evolution and temperature-dependences observed macroscopically. The remarkable correspondence in the dynamics of a quantum material and a quantum simulation opens the way to an understanding of emergent behaviour in diverse interacting many-body quantum systems at the microscopic level.
Abstract A finite length ferromagnetic chain with opposite spin polarization 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) characterizing 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.
We study the nonequilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterized by white noise correlation dynamics. We establish prethermalization in this model, showing that the quench dynamics of the on-site transverse magnetization first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast toward an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterized by spins with opposite transverse magnetization. We observe at intermediate timescales a phenomenology akin to Anderson localization: energy remains localized within the two domain walls, until the Markovian noise destroys coherence and, accordingly, disorder-induced localization, allowing the system to relax toward the late stages of its nonequilibrium dynamics. We compare our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the prethermal plateau is a generic property of spin chains with weak noise, while the phenomenon of prethermal Anderson localization is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system.
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.