The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.
The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.
When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize despite strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium with respect to the Hamiltonian. Using experimental and numerical methods we observe the essential signatures of MBL: initial state memory retention, Poissonian distributed many-body energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where detailed modeling of MBL becomes impossible.
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.
Classical statistical mechanics relies on the ergodic hypothesis, which states that a system explores the entire allowed phase space during its time evolution. Pure quantum states are at odds with this concept as they remain in a single quantum state even if the system's parameters are suddenly altered. However, in a generic many-body system, coherent dynamics drive local thermalization of its subsystems. In this case, any local observable appears thermal and can be described by a statistical ensemble even though the full state remains pure. The key to understanding the phenomenon of quantum thermalization lies in the entanglement properties of the system: The presence of entanglement creates local entropy that validates the use of statistical physics.\nIn this thesis, we experimentally study the emergence of statistical mechanics in a quantum state and observe the fundamental role of quantum entanglement in facilitating this emergence. We perform microscopy on an evolving quantum system, and we see thermalization occur on a local scale while we measure that the full quantum state remains pure.\nThe only known robust exception from the paradigm of quantum thermalization is provided by disordered systems. In this case, the particle transport ceases through the system, preventing the formation of a sufficient amount of entanglement required for thermalization. However, if the many-body system is interacting, the state develops non-local quantum correlations that are inaccessible to any local observable. These correlations spread exponentially slowly in time throughout the entire system and are considered a hallmark feature of many-body-localized states.\nIn order to study the interplay between thermalization and localization in our system, we develop novel methods for high fidelity state preparation and readout. We achieved an exquisite isolation of our system from the environment, which allows us to monitor coherent many-body dynamics over multiple decades of time evolution.\nWe experimentally realize such a many-body localized system and observe the formation of non-local quantum correlations, while the particle transport is frozen in the system. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.
An interacting quantum system that is subject to disorder may cease to thermalize owing to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to understanding this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy, the hallmark of many-body localization. Our work experimentally establishes many-body localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems.