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arXiv:2603.12236

Onset of Ergodicity Across Scales on a Digital Quantum Processor

Faisal Alam, Marcos Crichigno, Elizabeth Crosson, Steven T. Flammia, Filippo Maria Gambetta, Max Hunter Gordon, Michael Kreshchuk, Ashley Montanaro, Alberto Nocera, Raul A. Santos

quant-phcond-mat.dis-nnSubmitted Mar 12, 2026• Announced Mar 13, 2026• 0 citations
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Abstract

Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on IBM's Nighthawk superconducting processor, reaching system sizes of up to $10\times10$ qubits. We probe ergodicity across different length scales by coarse-graining the system into spatial patches of varying sizes and introducing a measure based on the collision entropy of each patch, enabling a detailed study of when ergodic behavior emerges across scales. The high sampling rate of superconducting quantum processing units, together with an optimal sample estimator, allow us to access patches of sizes up to $3\times3$. We observe that as the Heisenberg coupling $J$ increases, the noiseless system undergoes a smooth crossover from subergodic to ergodic behavior, with smaller patches approaching their random-matrix-theory values first, thereby revealing a hierarchy across scales. In the region of parameter space where classical tensor-network simulations are reliable, small patches or small values of $J$, we find excellent agreement with the error-mitigated quantum simulation. Beyond this regime, volume-law entanglement and contraction complexity growth causes the cost of classical methods to rise sharply. Our results open new directions for the use of quantum computers in the study of quantum thermalization.

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Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on IBM's Nighthawk superconducting processor, reaching system sizes of up to 10×1010\times1010×10 qubits. We probe ergodicity across different length scales by coarse-graining the system into spatial patches of varying sizes and introducing a measure based on the collision entropy of each patch, enabling a detailed study of when ergodic behavior emerges across scales. The high sampling rate of superconducting quantum processing units, together with an optimal sample estimator, allow us to access patches of sizes up to 3×33\times33×3. We observe that as the Heisenberg coupling JJJ increases, the noiseless system undergoes a smooth crossover from subergodic to ergodic behavior, with smaller patches approaching their random-matrix-theory values first, thereby revealing a hierarchy across scales. In the region of parameter space where classical tensor-network simulations are reliable, small patches or small values of JJJ, we find excellent agreement with the error-mitigated quantum simulation. Beyond this regime, volume-law entanglement and contraction complexity growth causes the cost of classical methods to rise sharply. Our results open new directions for the use of quantum computers in the study of quantum thermalization.
Many-body localization (MBL) provides a mechanism by which interacting quantum systems evade thermalization, leading to persistent memory of initial conditions and slow entanglement growth. Probing these dynamical signatures in large systems and at long evolution times remains challenging for both classical simulations and current quantum devices. Here we experimentally investigate the ergodic-MBL crossover in quasiperiodic Floquet Ising systems using up to 144 qubits on an IBM Quantum processor. By implementing deep Floquet circuits reaching up to 5000 cycles, we access long-time many-body dynamics beyond the regime explored in previous quantum computing experiments. Measurements of autocorrelation functions reveal a smooth crossover from rapid thermalization at weak quasiperiodic potential strength to persistent correlations in the strong-disorder regime. Notably, in addition to the one-dimensional system, we also observe clear signatures consistent with localization behavior in the two-dimensional system. Furthermore, the quantum Fisher information exhibits logarithmic growth over thousands of Floquet cycles, providing evidence for slow entanglement spreading characteristic of the MBL regime. These results demonstrate that programmable quantum processors can serve as experimental platforms for probing nonergodic quantum many-body dynamics and exploring localization phenomena in regimes beyond the reach of classical simulations.
Periodically driven interacting quantum many-body systems can exhibit long-lived prethermal dynamics, where local observables retain coherent structure even as entanglement and operator complexity grow. Accessing this regime at the system sizes and times needed to determine physical properties of the prethermal state remains a central challenge: state-of-the-art classical methods become unreliable, while noise in quantum hardware degrades observable expectation values. Here we overcome these limitations for a Floquet Ising magnet realized on a heavy-hex lattice. Using the advanced error mitigation software QESEM on an IBM Heron r3 superconducting quantum processor, we measure magnetization dynamics with percent-level precision and resolve long-lived subharmonic prethermal oscillations in systems of up to 74 qubits. These experiments reach regimes for which leading tensor-network simulations fail to converge, while sparse Pauli-path simulations remain strongly truncation dependent despite extensive computations on advanced GPUs and the Fugaku supercomputer. Leveraging this quantum-accessible regime, we extend finite-size scaling to larger systems and find an unexpectedly slow decrease of the oscillation amplitude with system size, providing strong evidence that this oscillatory response persists in the thermodynamic limit of heavy-hex ladders. A hierarchy of mitigation and validation tests, including unbiased error mitigation, agreement between independent mitigation estimators, noise-model validation on the superconducting hardware, and cross-platform corroboration at selected Floquet cycles on Quantinuum System Model H2 and Quantinuum Helios trapped-ion hardware, supports the reliability of these findings. Our work establishes error-mitigated quantum processors as quantitative scientific instruments for discovering new physics in non-equilibrium quantum matter.
Abstract Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase , in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.
Quantum many-body systems display an extraordinary degree of complexity, yet many of their features are universal: they depend not on microscopic details, but on a few fundamental physical aspects such as symmetries. A central challenge is to distill these universal characteristics from model-specific ones. Random quantum states sampled from a uniform distribution, the Haar measure, provide a powerful framework for capturing this typicality. Here, we experimentally study the entanglement and symmetries of random many-body quantum states generated by evolving simple product states under ergodic Floquet models. We find excellent agreement with the predictions from the Haar-random state ensemble. First, we measure the Rényi-2 entanglement entropy as a function of the subsystem size, observing the Page curve. Second, we probe the subsystem symmetries using entanglement asymmetry. Finally, we measure the moments of partially transposed reduced density matrices obtained by tracing out part of the system in the generated ensembles, thereby revealing distinct entanglement phases. Our results offer an experimental perspective on the typical entanglement and symmetries of many-body quantum systems.
Abstract Emulating thermal observables on a digital quantum computer is essential for quantum simulation of many-body physics. However, thermalization typically requires a large system size due to incorporating a thermal bath, whilst limited resources of near-term digital quantum processors allow for simulating relatively small systems. We show that thermal observables and fluctuations may be obtained for a small closed system without a thermal bath. Thermal observables occur upon classically averaging quantum mechanical observables over randomized variants of their time evolution that run independently on a digital quantum processor. Using an IBM quantum computer, we experimentally find thermal occupation probabilities with finite positive and negative temperatures defined by the initial state’s energy. Averaging over random evolutions facilitates error mitigation, with the noise contributing to the temperature in the simulated observables. This result fosters probing the dynamical emergence of equilibrium properties of matter at finite temperatures on noisy intermediate-scale quantum hardware.
The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.