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

arXiv:2408.00069 · Nature Communications

Quantum computing universal thermalization dynamics in a (2 + 1)D Lattice Gauge Theory

Niklas Mueller, Tianyi Wang, Or Katz, Zohreh Davoudi, Marko Cetina

Published Jul 1, 2025• 18 citations
arXivHTMLPDF

Abstract

lattice gauge theory in 2+1 spacetime dimensions. Using randomized-measurement protocols, we efficiently learn a classical approximation of non-equilibrium states that yields the gap-ratio distribution and the spectral form factor of the entanglement Hamiltonian. These observables exhibit universal early-time signals for quantum chaos, a prerequisite for thermalization. Our work, therefore, establishes quantum computers as robust tools for studying universal features of thermalization in complex many-body systems, including in gauge theories.

DOI
10.1038/s41467-025-60177-7

Related papers

Quantum thermalization of gauge theories: chaos, turbulence and universality

Niklas Mueller, Torsten V. Zache, R.J. Ott

In this talk, we discuss real-time thermalization dynamics of $\mathbf{Z}_2$ Lattice Gauge Theory in 2+1 spacetime dimensions. While classical thermalization is commonly associated with chaotic behavior, turbulence and universality, the manifestation of these phenomena in quantum mechanical systems is not clear. However, when viewed through the lens of Entanglement Structure, we find that quantum thermalization proceeds in characteristic stages and reveals phenomena remarkably similar to their classical counterparts: chaos, turbulence and universality.

arXiv:2111.01155•International Symposium on Lattice Field Theory (LATTICE)•May 16, 2022•0 citations

Lattice Gauge Theory: Discretized Quantum Fields and Thermalization Dynamics — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Lattice gauge theory (LatticeQCD.jl, 2+1D gauge theories, disorder-free localization, thermalization) computes non-perturbative quantum field dynamics via discretized spacetime grids, with recent focus on quantum simulation of gauge fields. | MATH: Lattice discretization replaces continuous gauge group SU(3) (QCD) with finite-dimensional link variables \(U_\mu(x) \in SU(3)\); Wilson action \(S_W = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{N} \text{Re Tr}\, U_{\square}\right)\), \(\beta = 2N/g^2\); for 2+1D gauge theory, coupling \(g^2\) has mass dimension 1, dimensionless ratio \(g^2 a\) (lattice spacing \(a\)); disorder-free localization arises from Hilbert-space fragmentation — conserved quantities from Gauss's law \(\nabla \cdot E = \rho\) on lattice; thermalization studied via entanglement entropy \(S = -\text{Tr}(\rho \log \rho)\) and spectral form factor \(g(\tau) = |Z(\beta + i\tau)/Z(\beta)|^2\). | CONNECTION: Lattice gauge theory is inherently a **root-system Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

•Sep 6, 2026•0 citations

Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory

Niklas Mueller, Joseph Carolan, Andrew Connelly +3 more

Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

arXiv:2210.03089•Oct 6, 2022•0 citations

Thermalization of Gauge Theories from their Entanglement Spectrum

Niklas Mueller, Torsten V. Zache, R.J. Ott

Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the entanglement structure of Z_{2} lattice gauge theory in (2+1) spacetime dimensions. We demonstrate Li and Haldane's conjecture, and show consistency of the entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying nonequilibrium dynamics after a quench, we provide an extensive description of thermalization in Z_{2} gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients α=0.8±0.2 and β=0.0±0.1 at intermediate times, and finally thermal saturation of the von Neumann entropy.

arXiv:2107.11416•Physical Review Letters•Jun 27, 2022•47 citations

Lattice gauge theories and constrained systems: from quantum simulation to non-equilibrium dynamics

Federica Maria Surace

In the last decade the non-equilibrium dynamics of isolated quantum systems has raised a huge interest for both its conceptual and practical implications. Simulation of quantum dynamics represents by now a very active research effort, with highly controllable quantum devices composed of hundreds of qubits already being realized in numerous setups. These offer the unprecedented possibility to access real-time quantum dynamics and strongly correlated quantum many-body states, opening numerous avenues not only for future quantum technologies, but also for long-standing theoretical problems. One of the most sought-after applications is the computation of real-time evolution in theories of fundamental interactions. Since Wilson's proposal in 1974, the equilibrium phase diagrams of lattice gauge theories have been successfully investigated with Monte Carlo simulations in a wide range of parameters. Nonequilibrium properties, on the other hand, cannot be accessed with conventional techniques. Thanks to the recent advances in numerics (e.g. tensor networks) and experiments (quantum simulation), new promising tools are now available for tackling these questions. Remarkable works have already demonstrated that applying these techniques to simple theories, such as one-dimensional quantum electrodynamics, can help to detect the signatures of confinement and pair creation. Despite these impressive achievements, investigating the non-equilibrium dynamics of gauge theories with quantum simulators turned out to be extremely challenging. This is mostly due to the complex constrained dynamics of these theories, which make their simulation with realistic atomic platforms particularly difficult. At the same time, the dynamical constraints can play a key role in determining novel interesting phenomena and peculiar non-equilibrium properties. These phenomena -- which include, for example, quantum scars, fractons, Hilbert space fragmentation -- can lead to anomalous dynamics, eventually evading the paradigm of thermalization, which predicts the relaxation of physical observable to their thermodynamic values. The aim of this thesis is twofold: first, we want to address through a combination of numerical and analytical tools some of the open questions regarding the non-equilibrium dynamics of quantum many-body systems with constrained Hilbert spaces, including lattice gauge theories. In addition, the work reported here is part of a large effort of the community towards the quantum simulation of complex phenomena of condensed matter and high-energy physics.

•Sep 29, 2021•0 citations

Quantum Computation of Dynamical Quantum Phase Transitions and Entanglement Tomography in a Lattice Gauge Theory

Niklas Mueller, Joseph Carolan, Andrew Connelly +3 more

A quantum computer helps illuminate the physics of the early Universe and of hadron and ion colliders by solving for the nonequal time correlations and performing entanglement tomography of a strongly coupled gauge theory far from equilibrium.

PRX Quantum•Aug 18, 2023•60 citations
lattice gauge theory in 2+1 spacetime dimensions. Using randomized-measurement protocols, we efficiently learn a classical approximation of non-equilibrium states that yields the gap-ratio distribution and the spectral form factor of the entanglement Hamiltonian. These observables exhibit universal early-time signals for quantum chaos, a prerequisite for thermalization. Our work, therefore, establishes quantum computers as robust tools for studying universal features of thermalization in complex many-body systems, including in gauge theories.
In this talk, we discuss real-time thermalization dynamics of Z2\mathbf{Z}_2Z2​ Lattice Gauge Theory in 2+1 spacetime dimensions. While classical thermalization is commonly associated with chaotic behavior, turbulence and universality, the manifestation of these phenomena in quantum mechanical systems is not clear. However, when viewed through the lens of Entanglement Structure, we find that quantum thermalization proceeds in characteristic stages and reveals phenomena remarkably similar to their classical counterparts: chaos, turbulence and universality.
FINDING: Lattice gauge theory (LatticeQCD.jl, 2+1D gauge theories, disorder-free localization, thermalization) computes non-perturbative quantum field dynamics via discretized spacetime grids, with recent focus on quantum simulation of gauge fields. | MATH: Lattice discretization replaces continuous gauge group SU(3) (QCD) with finite-dimensional link variables Uμ(x)∈SU(3)U_\mu(x) \in SU(3)Uμ​(x)∈SU(3); Wilson action SW=β∑plaquettes(1−1NRe Tr U□)S_W = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{N} \text{Re Tr}\, U_{\square}\right)SW​=β∑plaquettes​(1−N1​Re TrU□​), β=2N/g2\beta = 2N/g^2β=2N/g2; for 2+1D gauge theory, coupling g2g^2g2 has mass dimension 1, dimensionless ratio g2ag^2 ag2a (lattice spacing aaa); disorder-free localization arises from Hilbert-space fragmentation — conserved quantities from Gauss's law ∇⋅E=ρ\nabla \cdot E = \rho∇⋅E=ρ on lattice; thermalization studied via entanglement entropy S=−Tr(ρlog⁡ρ)S = -\text{Tr}(\rho \log \rho)S=−Tr(ρlogρ) and spectral form factor g(τ)=∣Z(β+iτ)/Z(β)∣2g(\tau) = |Z(\beta + i\tau)/Z(\beta)|^2g(τ)=∣Z(β+iτ)/Z(β)∣2. | CONNECTION: Lattice gauge theory is inherently a **root-system Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.
Using dual theories embedded into a larger unphysical Hilbert space along entanglement cuts, we study the entanglement structure of Z_{2} lattice gauge theory in (2+1) spacetime dimensions. We demonstrate Li and Haldane's conjecture, and show consistency of the entanglement Hamiltonian with the Bisognano-Wichmann theorem. Studying nonequilibrium dynamics after a quench, we provide an extensive description of thermalization in Z_{2} gauge theory which proceeds in a characteristic sequence: Maximization of the Schmidt rank and spreading of level repulsion at early times, self-similar evolution with scaling coefficients α=0.8±0.2 and β=0.0±0.1 at intermediate times, and finally thermal saturation of the von Neumann entropy.
In the last decade the non-equilibrium dynamics of isolated quantum systems has raised a huge interest for both its conceptual and practical implications. Simulation of quantum dynamics represents by now a very active research effort, with highly controllable quantum devices composed of hundreds of qubits already being realized in numerous setups. These offer the unprecedented possibility to access real-time quantum dynamics and strongly correlated quantum many-body states, opening numerous avenues not only for future quantum technologies, but also for long-standing theoretical problems. One of the most sought-after applications is the computation of real-time evolution in theories of fundamental interactions. Since Wilson's proposal in 1974, the equilibrium phase diagrams of lattice gauge theories have been successfully investigated with Monte Carlo simulations in a wide range of parameters. Nonequilibrium properties, on the other hand, cannot be accessed with conventional techniques. Thanks to the recent advances in numerics (e.g. tensor networks) and experiments (quantum simulation), new promising tools are now available for tackling these questions. Remarkable works have already demonstrated that applying these techniques to simple theories, such as one-dimensional quantum electrodynamics, can help to detect the signatures of confinement and pair creation. Despite these impressive achievements, investigating the non-equilibrium dynamics of gauge theories with quantum simulators turned out to be extremely challenging. This is mostly due to the complex constrained dynamics of these theories, which make their simulation with realistic atomic platforms particularly difficult. At the same time, the dynamical constraints can play a key role in determining novel interesting phenomena and peculiar non-equilibrium properties. These phenomena -- which include, for example, quantum scars, fractons, Hilbert space fragmentation -- can lead to anomalous dynamics, eventually evading the paradigm of thermalization, which predicts the relaxation of physical observable to their thermodynamic values. The aim of this thesis is twofold: first, we want to address through a combination of numerical and analytical tools some of the open questions regarding the non-equilibrium dynamics of quantum many-body systems with constrained Hilbert spaces, including lattice gauge theories. In addition, the work reported here is part of a large effort of the community towards the quantum simulation of complex phenomena of condensed matter and high-energy physics.