We present several discoveries in quantum many-body dynamics and their applications. We discover types of universal randomness that emerge in many-body dynamics, now known as "deep thermalization" and "Hilbert space ergodicity." These discoveries have been enabled by recent advances in programmable quantum simulators, in particular their capability to perform measurements with unprecedented precision in both space and time. This universality allows for a number of practical applications adapted from the quantum information literature, including benchmarking, noise channel learning and state tomography. These applications rely on naturally-realized quantum dynamics and do not require fine-tuned controls. Hence, they are applicable to analog quantum simulators, and we realize several of these protocols in experiment. These results in emergent randomness are broadly applicable to generic many-body systems. We also discover new structures in specific systems realized in modern experimental platforms, namely in a lattice gauge theory realized in neutral atom arrays, and in optical lattice quantum gas microscopes. Finally, we identify a new type of structure present in the emergent randomness, governed by the presence of anti-unitary symmetries. Together, these results advance our understanding of quantum many-body dynamics and illustrate that much remains to be discovered in this active field of research.
We present several discoveries in quantum many-body dynamics and their applications. We discover types of universal randomness that emerge in many-body dynamics, now known as "deep thermalization" and "Hilbert space ergodicity." These discoveries have been enabled by recent advances in programmable quantum simulators, in particular their capability to perform measurements with unprecedented precision in both space and time. This universality allows for a number of practical applications adapted from the quantum information literature, including benchmarking, noise channel learning and state tomography. These applications rely on naturally-realized quantum dynamics and do not require fine-tuned controls. Hence, they are applicable to analog quantum simulators, and we realize several of these protocols in experiment. These results in emergent randomness are broadly applicable to generic many-body systems. We also discover new structures in specific systems realized in modern experimental platforms, namely in a lattice gauge theory realized in neutral atom arrays, and in optical lattice quantum gas microscopes. Finally, we identify a new type of structure present in the emergent randomness, governed by the presence of anti-unitary symmetries. Together, these results advance our understanding of quantum many-body dynamics and illustrate that much remains to be discovered in this active field of research.
Recent advances in quantum simulation have enabled the discovery of novel forms of universality in quantum many-body dynamics. In this Review, we discuss deep thermalization and Hilbert space ergodicity--two recently discovered phenomena characterized by the emergence of distributions of quantum states that are "maximally random" in a precise sense. They offer a new perspective on how irreversible statistical mechanics arises from reversible unitary quantum dynamics, going beyond conventional theories of quantum thermalization and equilibration. We review a unifying framework, rooted in quantum information theory and principles of maximum entropy, that explains the different forms of ergodicity which arise under various physical constraints. We discuss open questions and active research directions, including generalizations beyond ensembles of pure quantum states, phase transitions in deep thermalization tied to deeper forms of ergodicity-breaking, connections to broader topics in quantum thermalization and ergodicity, and applications in quantum information science, such as for benchmarking or tomography.
Chaotic quantum many-body dynamics typically lead to relaxation of local observables. In this process, known as quantum thermalization, a subregion reaches a thermal state due to quantum correlations with the remainder of the system, which acts as an intrinsic bath. While the bath is generally assumed to be unobserved, modern quantum science experiments have the ability to track both subsystem and bath at a microscopic level. Here, by utilizing this ability, we discover that measurement results associated with small subsystems exhibit universal random statistics following chaotic quantum many-body dynamics, a phenomenon beyond the standard paradigm of quantum thermalization. We explain these observations with an ensemble of pure states, defined via correlations with the bath, that dynamically acquires a close to random distribution. Such random ensembles play an important role in quantum information science, associated with quantum supremacy tests and device verification, but typically require highly-engineered, time-dependent control for their preparation. In contrast, our approach uncovers random ensembles naturally emerging from evolution with a time-independent Hamiltonian. As an application of this emergent randomness, we develop a benchmarking protocol which estimates the many-body fidelity during generic chaotic evolution and demonstrate it using our Rydberg quantum simulator. Our work has wide ranging implications for the understanding of quantum many-body chaos and thermalization in terms of emergent randomness and at the same time paves the way for applications of this concept in a much wider context.
Recent studies of "deep thermalization" have revealed universal physics in quantum many-body dynamics beyond equilibration towards Gibbs states: maximally random quantum state ensembles can emerge on local subsystems, generated by measurements on their complement. In this work, we further identify a new form of universality exhibited in the "finer fingerprints" of quantum dynamics for local subsystems, induced by global unitary time-evolution. Specifically, we consider the projected Kraus ensemble, an ensemble of Kraus operators obtained by unraveling the quantum channel on a small subsystem with respect to knowledge of the classical configurations of its complement. Our central result is a one-parameter random matrix Ansatz that captures the ensemble's emergent statistical behavior along particular spacetime scalings, valid for generic 1D circuit dynamics without conservation laws: the ensemble is described by the product of a complex Ginibre random matrix and an independent log-normal random real scalar. The former encodes scrambling within the subsystem, captured by rotational invariance of the Ginibre measure, whereas the latter encodes fluctuations in the Born probabilities, arising from locality of the underlying dynamics. Our Ansatz can be established in the special cases of dynamics generated by global Haar random unitaries and dual-unitary circuits, while we motivate it for generic circuits using arguments of spacetime duality and the multiplicative ergodic theorem on long products of spatial transfer matrices. Extensive numerical simulations for random and Floquet circuit models verify these predictions. This universality in Kraus operators also provides a microscopic mechanism for deep thermalization in generic 1D quantum circuit dynamics, and has implications for local quantum information recoverability involving classical side information tied to knowledge of the bath.
Quantum chaos concerns the emergence of universal statistical and dynamical prop- erties in quantum systems whose classical counterparts exhibit chaotic behavior. Unlike classical chaos, which can be characterized by sensitivity to initial conditions and exponential divergence of trajectories, quantum chaos manifests itself through a variety of indirect diagnostics, including spectral correlations, operator growth, and information scrambling. Understanding how these signatures arise from microscopic dynamics, and how they can be accessed in realistic many-body systems, is a central challenge in modern physics. This thesis investigates quantum chaos from complementary theoretical and practical perspectives. On the theoretical side, it develops effective descriptions of chaotic dy- namics in many-body systems with approximate symmetries, focusing on how weak symmetry breaking controls the exploration of Hilbert space and the crossover to random-matrix universality. Using perturbative arguments, numerical simulations, and a nonlinear sigma-model formulation, we identify a regime of Hilbert-space dif- fusion in which chaotic dynamics unfolds through a slow, collective spreading across nearly decoupled symmetry sectors. On the practical side, the thesis addresses the question of how paradigmatic chaotic models can be realized and probed in controlled experimental platforms. In partic- ular, it explores quantum simulation schemes for Sachdev–Ye–Kitaev (SYK) models using cavity quantum electrodynamics. By employing time-dependent disorder and Trotterized evolution in single-mode optical cavities, we demonstrate how low-rank interactions can be systematically promoted to effective all-to-all randomness, re- producing the spectral and dynamical signatures of SYK physics. Extensions to open-system dynamics are discussed, including Lindbladian realizations and the role of dissipation. The thesis thus highlights the connections between effective descriptions of quantum chaos and their implementation in controlled quantum simulation settings.
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. Published by the American Physical Society 2024
Quantum circuits—built from local unitary gates and local measurements—are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far from equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as dynamical phase transitions in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.