Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Tuning canonical typicality by quantum chaos

Mahdi Kourehpaz, Stefan Donsa, Fabian Lackner, Joachim Burgdörfer, Iva Březinová

Published Mar 10, 2021• 0 citations
OpenAlex

Abstract

One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic ($N \rightarrow \infty$) limit the density matrix emerges for small subsystems from almost all pure states of large quantum many-body systems. This notion of canonical is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. We show that quantum chaos plays a crucial role in the emergence of typicality for large but finite quantum systems. We demonstrate that the degree of typicality can be quantitatively controlled and tuned by the degree of quantum chaoticity present in the many-body system.

Related papers

Canonical Density Matrices from Eigenstates of Mixed Systems

Mahdi Kourehpaz, Stefan Donsa, Fabian Lackner +2 more

One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.

arXiv:2103.05974•Entropy•Nov 29, 2022•5 citations

Quantum chaos at finite temperature in local spin Hamiltonians

Christopher M. Langlett, Cheryne Jonay, Vedika Khemani +1 more

Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes, quantum chaos has been primarily understood through the correspondence between the eigensystem statistics of midspectrum eigenstates and the universal statistics described by random matrix theory (RMT). However, this correspondence no longer holds for finite-temperature eigenstates. Here we show that the statistical properties of finite-temperature eigenstates of quantum chaotic Hamiltonians can be accurately described by pure random states constrained by a local charge, with the average charge density of the constrained random state ensemble playing the same role as the average energy density of the eigenstates. By properly normalizing the energy density using a single Hamiltonian-dependent parameter that quantifies the typical energy per degree of freedom, we find excellent agreement between the entanglement entropy statistics of eigenstates and that of constrained random states. Interestingly, in small pockets of Hamiltonian parameter phase space which we previously identified as `maximally chaotic' [PRX 14, 031014 (2024)], we find excellent agreement not only at the level of the first moment, including O(1) corrections, but also at the level of statistical fluctuations. These results show that notions of maximal chaos -- in terms of how much randomness eigenstates contain -- can still be defined at finite temperature in physical Hamiltonian models away from semi-classical and large-$N$ limits.

arXiv:2501.13164•Jan 22, 2025•0 citations

Thermalization in a closed quantum system from randomized dynamics

Nikolay V. Gnezdilov, Andrei I. Pavlov

The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.

cond-mat.stat-mechCross-listedarXiv:2601.00056•Jan 2, 2026•0 citations

Statistical mechanics from relational complex time with a pure state

Sebastian Gemsheim, Jan Michael Rost

Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigenstates of a system and its environment, analyzing their cardinality. We show that the canonical density for a system emerges from a maximally entangled global state of system and environment through relational complex time evolution between system and environment without the need to maximize the entropy or to count states. Published by the American Physical Society 2024

arXiv:2405.06401•Physical review. D/Physical review. D.•Jun 3, 2024•3 citations

Necessity of entanglement for the typicality argument in statistical mechanics

Pedro Silva Correia, Gabriel Dias Carvalho, Thiago Rodrigues de Oliveira

Typicality arguments replace the postulated mixed state ensembles of statistical mechanics with pure states sampled uniformly at random, explaining why most microstates of large systems exhibit thermal behavior. This paradigm has been revived in quantum contexts, where entanglement is deemed essential, but no clear quantitative link between entanglement structure and typicality has been established. Here, we study pure quantum states with controlled multipartite entanglement and show that when entanglement grows with system size $N$, fluctuations in macroscopic observables decay exponentially with $N$, whereas if entanglement remains finite, one recovers only the classical $1/\sqrt{N}$ suppression. Our work thus provides a quantitative connection between entanglement structure and the emergence of typicality, demonstrating that entanglement is crucial for thermalization in small quantum systems but unnecessary to justify equilibrium in macroscopic ensembles. This unifies classical and quantum foundations of statistical mechanics by pinpointing exactly when and why entanglement matters.

arXiv:2504.21090•Physical Review A•May 21, 2026•0 citations

Emergent Randomness and Benchmarking from Many-Body Quantum Chaos

Joonhee Choi, Adam L. Shaw, Ivaylo S. Madjarov +10 more

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.

•Mar 5, 2021•6 citations
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞N \rightarrow \inftyN→∞) limit the density matrix emerges for small subsystems from almost all pure states of large quantum many-body systems. This notion of canonical is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. We show that quantum chaos plays a crucial role in the emergence of typicality for large but finite quantum systems. We demonstrate that the degree of typicality can be quantitatively controlled and tuned by the degree of quantum chaoticity present in the many-body system.
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.
Understanding the emergence of chaos in many-body quantum systems away from semi-classical limits, particularly in spatially local interacting spin Hamiltonians, has been a long-standing problem. In these intrinsically quantum regimes, quantum chaos has been primarily understood through the correspondence between the eigensystem statistics of midspectrum eigenstates and the universal statistics described by random matrix theory (RMT). However, this correspondence no longer holds for finite-temperature eigenstates. Here we show that the statistical properties of finite-temperature eigenstates of quantum chaotic Hamiltonians can be accurately described by pure random states constrained by a local charge, with the average charge density of the constrained random state ensemble playing the same role as the average energy density of the eigenstates. By properly normalizing the energy density using a single Hamiltonian-dependent parameter that quantifies the typical energy per degree of freedom, we find excellent agreement between the entanglement entropy statistics of eigenstates and that of constrained random states. Interestingly, in small pockets of Hamiltonian parameter phase space which we previously identified as `maximally chaotic' [PRX 14, 031014 (2024)], we find excellent agreement not only at the level of the first moment, including O(1) corrections, but also at the level of statistical fluctuations. These results show that notions of maximal chaos -- in terms of how much randomness eigenstates contain -- can still be defined at finite temperature in physical Hamiltonian models away from semi-classical and large-NNN limits.
The emergence of statistical mechanics from quantum dynamics is conventionally understood through quantum chaos, the Eigenstate Thermalization Hypothesis (ETH), and canonical typicality, which together explain the thermal behavior of local observables in quantum many-body systems. We provide a distinct mechanism in which, for a quantum many-body system under strong random perturbation, the chaotic behavior of the system's eigenvectors and a constraint on the total energy directly generate a canonical ensemble for the entire system. The canonical ensemble occurs as the first moment of the Porter-Thomas distribution of the system's chaotic eigenstates, and the constraint on the total energy sets the temperature in the ensemble. This yields canonically distributed expectation values without invoking ETH, a microcanonical ensemble, or a subsystem-bath partition for local and global observables. We numerically demonstrate the mechanism for the 1D transverse-field Ising model by showing canonically distributed eigenstate projectors and spin-spin correlators with distinctive temperature dependence of the correlation length. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigenstates of a system and its environment, analyzing their cardinality. We show that the canonical density for a system emerges from a maximally entangled global state of system and environment through relational complex time evolution between system and environment without the need to maximize the entropy or to count states. Published by the American Physical Society 2024
Typicality arguments replace the postulated mixed state ensembles of statistical mechanics with pure states sampled uniformly at random, explaining why most microstates of large systems exhibit thermal behavior. This paradigm has been revived in quantum contexts, where entanglement is deemed essential, but no clear quantitative link between entanglement structure and typicality has been established. Here, we study pure quantum states with controlled multipartite entanglement and show that when entanglement grows with system size NNN, fluctuations in macroscopic observables decay exponentially with NNN, whereas if entanglement remains finite, one recovers only the classical 1/N1/\sqrt{N}1/N​ suppression. Our work thus provides a quantitative connection between entanglement structure and the emergence of typicality, demonstrating that entanglement is crucial for thermalization in small quantum systems but unnecessary to justify equilibrium in macroscopic ensembles. This unifies classical and quantum foundations of statistical mechanics by pinpointing exactly when and why entanglement matters.
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.