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arXiv:2503.21553 · Nature

Prethermalization by random multipolar driving on a 78-qubit processor

Zheng-He Liu, Yu Liu, Gui-Han Liang, Cheng-Lin Deng, Keyang Chen, Yun‐Hao Shi, Tian-Ming Li, L. M. Zhang, B. Chen, Cai-Ping Fang, Da’er Feng, Xu-Yang Gu, Yang He, Kaixuan Huang, Hao Li, Hao-Tian Liu, Li Li, Zheng-Yang Mei, Zhen-Yu Peng, Jiacheng Song, Ming-Chuan Wang, Shuai-Li Wang, Ziting Wang, Yong-Xi Xiao, Min Xu, Yue-Shan Xu, Yu Yan, Yi-Han Yu, Wei-Ping Yuan, Jiachi Zhang, Junjie Zhao, Kui Zhao, Si-Yun Zhou, Zheng‐An Wang, Xiaohui Song, Ye F. Tian, Florian Mintert, Johannes Knolle, Roderich Moessner, Yu-Ran Zhang, Pan Zhang, Zhongcheng Xiang, Dongning Zheng, Kai Xu, Hongzheng Zhao, Heng Fan

Published Jan 28, 2026• 8 citations
arXivHTMLPDF

Abstract

Time-dependent drives hold promise for realizing non-equilibrium many-body phenomena that are absent in undriven systems1–3. Yet, drive-induced heating normally destabilizes the systems4,5, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives6,7. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Here, using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other way by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n + 1. Using quantum-state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a two-dimensional configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges. The existence of a long-lived, prethermal regime in many-body systems with tunable heating rates, driven by structured random protocols, is observed using a 78-qubit superconducting quantum processor.

DOI
10.1038/s41586-025-09977-x

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Time-dependent drives hold promise for realizing non-equilibrium many-body phenomena that are absent in undriven systems1–3. Yet, drive-induced heating normally destabilizes the systems4,5, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives6,7. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Here, using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other way by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n + 1. Using quantum-state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a two-dimensional configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges. The existence of a long-lived, prethermal regime in many-body systems with tunable heating rates, driven by structured random protocols, is observed using a 78-qubit superconducting quantum processor.
Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n+1. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges.
Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability with respect to random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are nonuniversal: we observe Fermi's golden rule scaling, power-law scaling inconsistent with the golden rule, and non-power-law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase the temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
Non-equilibrium dynamics of strongly and rapidly driven quantum many-body systems is poorly understood beyond periodic driving, where heating is exponentially slow in the drive frequency (Floquet Prethermalization). In contrast, non-periodic drives were found to exhibit widely different heating scalings with no unifying principle. This work identifies a resonance-suppression principle governing slow heating up to a prethermal lifetime τ∗τ_*τ∗​: When the drive's spectral arithmetic structure restricts multiphoton resonances, τ∗τ_*τ∗​ is controlled by low-frequency spectral suppression. The principle distinguishes (i) Single-photon suppression, quantified by a low-frequency suppression law f(Ω)f(Ω)f(Ω) for the drive's Fourier Transform weight near Ω=0Ω=0Ω=0, from (ii) Multi-photon suppression, where nested commutators remain controlled if exceptional arithmetic structure satisfies a subadditive property. Remarkably, if multi-photon suppression holds, τ∗τ_*τ∗​ scaling with drive speed λλλ is governed by f(Ω)f(Ω)f(Ω). This law of τ∗τ_*τ∗​ is found through a small-divisor mechanism in this work's iterative rotating frame scheme. Multi-photon suppression breakdown separates λλλ-scaling of τ∗τ_*τ∗​ in linear response and non-perturbative theory, shown by a case study of Quasi-Floquet driving. The principle is applied to (i) Resolve inconsistencies in literature on non-periodic driving, and (ii) Provide design principles for engineering prethermal phases of matter in programmable quantum simulators, exemplified by new non-periodic `Factorial' drives with tunable τ∗τ_*τ∗​.
Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives. We demonstrate that the thermalization time scales as (1/T)^{2n+2}, where n is the multipolar order and T is the intrinsic time-scale associated with the drive. In the n→∞ limit, the drive becomes quasiperiodic and the thermalization time becomes exponentially long [∼exp(β/T)]. We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals.