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:2608.25696

Physics-informed quantum algorithms for glueball-like excitations in a $\mathbb{Z}_2$ lattice gauge theory

Dan-Bo Zhang

hep-latquant-phSubmitted Aug 26, 2026• Announced Aug 27, 2026• 0 citations
v1 · Aug 26, 2026v2 · Sep 3, 2026
arXivHTMLPDF

Abstract

Glueball spectroscopy with quantum computing requires both a correlated gauge vacuum and a systematic construction of its low-lying pure-gauge excitations. We develop a physics-informed quantum-computing framework for these tasks in a $(2+1)$-dimensional $\mathbb{Z}_2$ lattice gauge theory. We use the term \emph{glueball-like} for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. The central strategy is to organize the computation around the physical structure of the glueball-like state rather than to search a generic many-body excitation space. We prepare the gauge vacuum variationally and use Wilson-loop quantum subspace expansion to construct and characterize the low-lying excitations. Moreover, eigenvector continuation uses nearby ground states to capture the growing loop dressing without a rapidly enlarged Wilson-loop basis, while a Bethe--Salpeter-type radius quantifies the associated spatial broadening. We further use quench dynamics to probe nonequilibrium production. Although demonstrated in an Abelian model, the framework is built from gauge-invariant vacuum and excitation structures and is naturally transferable to non-Abelian lattice gauge theories.

Comments
11 pages, 6 figures, comments are welcome

Related papers

Observation of glueball excitations and string breaking in a $2+1$D $\mathbb{Z}_2$ lattice gauge theory on a trapped-ion quantum computer

Kaidi Xu, Umberto Borla, Kevin Hemery +4 more

A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a $\mathbb{Z}_2$ lattice gauge theory in $2+1$D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a $6 \times 5$ matter-site square lattice utilizing all $56$ available qubits to execute over $1000$ entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine $2+1$D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to $1+1$D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.

hep-latCross-listedarXiv:2604.07435•Apr 10, 2026•0 citations

Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

Luca Lumia, Pietro Torta, Glen Bigan Mbeng +4 more

We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.

arXiv:2112.11787•Dec 22, 2021•1 citation

Quantum Simulations of Two-Dimensional Non-Abelian Adjoint String Breaking

Anthony N. Ciavarella, Roland de Putter, Ed Younis +1 more

Quantum computers offer the potential to directly probe the dynamics of strongly coupled quantum field theories. As a step towards reaching this potential, local Krylov-based truncations of a pure SU(2) lattice gauge theory on a triangular lattice are constructed. Adjoint strings connected to dynamical gluons are constructed in this truncated theory, and the resonances dominating the long-term dynamics at a large value of the gauge coupling are determined. Local operators are constructed to identify string oscillations and breakings. This is used to perform a quantum simulation of adjoint string breaking on an $8\times8$ and $16\times8$-site lattice with ibm_boston using all 156 qubits. Quantitative agreement with tensor network simulations is obtained for circuits with 7,634 CZ gates with a two-qubit gate depth of 218. In this simulation, the rates of oscillations and glueball production are identified with a distinctly non-Abelian signature of the underlying gauge group.

hep-latCross-listedarXiv:2608.28752•Sep 1, 2026•0 citations

Dynamics of loops for SU(2) gauge theory in (2+1)-dimension

Aahiri Naskar

Pure gauge theories in more than one spatial dimension are extremely interesting as they allow pure gauge observables such as glueballs and Wilson loops. Simulating the real-time dynamics of pure non-Abelian lattice gauge theories poses a significant computational challenge due to the large number of spurious gauge degrees of freedom. This work presents a brute-force (exact diagonalization) study of 2+1-dimensional SU(2) lattice gauge theory, leveraging the gauge-invariant Loop-String-Hadron (LSH) framework. Using only CPU-based computation, we have successfully demonstrated classical simulation on systems of up to 9 plaquettes and aim to push it further by leveraging combinations of CPUs and GPUs. This work provides crucial benchmarks for GPU implementations, near-term tensor network simulators, and quantum simulations, opening a new avenue for studying fundamental phenomena like thermalization in a non-Abelian gauge theory directly from the Hamiltonian perspective in higher dimensions.

International Symposium on Lattice Field Theory (LATTICE)•Oct 11, 2026•0 citations

Cavity models of non-Abelian gauge theories

Lucia Valor, Jacquelin Luneau, Klaus Liegener +2 more

In quantum optics and related fields, cavity quantum electrodynamics provides a powerful framework for modeling the low-energy properties of bound charges coupled to electromagnetic fields, using a minimal set of atomic levels and isolated photonic modes. Here, we develop a similar framework for non-Abelian gauge theories, focusing on the pure-gauge dynamics of SU(2) fields as the conceptually simplest example. Starting from the corresponding Yang-Mills Lagrangian, we derive an SU(2) cavity Hamiltonian in the Coulomb gauge, represented in terms of only three localized bosonic modes. Unlike its non-interacting electromagnetic counterpart, this model exhibits a nontrivial excitation spectrum featuring bound composite gauge particles ('glueballs') as the lowest-energy configurations. We extend this framework to one-dimensional arrays of coupled SU(2) cavities and discuss the driven excitation of a glueball condensate and the clustering of multi-glueball states as two elementary interaction-induced processes in these models. These examples offer a glimpse into the multitude of novel many-body phenomena that arise within this cavity SU(2) framework and we show how this physics at the interface between particle physics and quantum optics can be experimentally explored using state-of-the-art superconducting quantum circuits.

quant-pharXiv:2610.27070•Oct 21, 2026

Time-Domain Observables for Resonant Scattering in Quantum Simulations of Lattice Gauge Theory

Praveen Balaji, Patrick Draper, Enrico Rinaldi

Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure $SU(3)$ lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model $\texttt{H2-2}$, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires $\sim 25n$ entangling gates for $n$ Trotter steps.

hep-latCross-listedarXiv:2610.17470•Oct 14, 2026•0 citations
Physics-informed quantum algorithms for glueball-like excitations in a Z2\mathbb{Z}_2Z2​ lattice gauge theory
Glueball spectroscopy with quantum computing requires both a correlated gauge vacuum and a systematic construction of its low-lying pure-gauge excitations. We develop a physics-informed quantum-computing framework for these tasks in a (2+1)(2+1)(2+1)-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory. We use the term \emph{glueball-like} for localized closed-flux excitations on the confining side of this Abelian model, without identifying them with the non-Abelian glueballs of QCD. The central strategy is to organize the computation around the physical structure of the glueball-like state rather than to search a generic many-body excitation space. We prepare the gauge vacuum variationally and use Wilson-loop quantum subspace expansion to construct and characterize the low-lying excitations. Moreover, eigenvector continuation uses nearby ground states to capture the growing loop dressing without a rapidly enlarged Wilson-loop basis, while a Bethe--Salpeter-type radius quantifies the associated spatial broadening. We further use quench dynamics to probe nonequilibrium production. Although demonstrated in an Abelian model, the framework is built from gauge-invariant vacuum and excitation structures and is naturally transferable to non-Abelian lattice gauge theories.
Observation of glueball excitations and string breaking in a 2+12+12+1D Z2\mathbb{Z}_2Z2​ lattice gauge theory on a trapped-ion quantum computer
A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a Z2\mathbb{Z}_2Z2​ lattice gauge theory in 2+12+12+1D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a 6×56 \times 56×5 matter-site square lattice utilizing all 565656 available qubits to execute over 100010001000 entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine 2+12+12+1D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to 1+11+11+1D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.
Two-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
We propose an implementation of a two-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.
Quantum computers offer the potential to directly probe the dynamics of strongly coupled quantum field theories. As a step towards reaching this potential, local Krylov-based truncations of a pure SU(2) lattice gauge theory on a triangular lattice are constructed. Adjoint strings connected to dynamical gluons are constructed in this truncated theory, and the resonances dominating the long-term dynamics at a large value of the gauge coupling are determined. Local operators are constructed to identify string oscillations and breakings. This is used to perform a quantum simulation of adjoint string breaking on an 8×88\times88×8 and 16×816\times816×8-site lattice with ibm_boston using all 156 qubits. Quantitative agreement with tensor network simulations is obtained for circuits with 7,634 CZ gates with a two-qubit gate depth of 218. In this simulation, the rates of oscillations and glueball production are identified with a distinctly non-Abelian signature of the underlying gauge group.
Pure gauge theories in more than one spatial dimension are extremely interesting as they allow pure gauge observables such as glueballs and Wilson loops. Simulating the real-time dynamics of pure non-Abelian lattice gauge theories poses a significant computational challenge due to the large number of spurious gauge degrees of freedom. This work presents a brute-force (exact diagonalization) study of 2+1-dimensional SU(2) lattice gauge theory, leveraging the gauge-invariant Loop-String-Hadron (LSH) framework. Using only CPU-based computation, we have successfully demonstrated classical simulation on systems of up to 9 plaquettes and aim to push it further by leveraging combinations of CPUs and GPUs. This work provides crucial benchmarks for GPU implementations, near-term tensor network simulators, and quantum simulations, opening a new avenue for studying fundamental phenomena like thermalization in a non-Abelian gauge theory directly from the Hamiltonian perspective in higher dimensions.
In quantum optics and related fields, cavity quantum electrodynamics provides a powerful framework for modeling the low-energy properties of bound charges coupled to electromagnetic fields, using a minimal set of atomic levels and isolated photonic modes. Here, we develop a similar framework for non-Abelian gauge theories, focusing on the pure-gauge dynamics of SU(2) fields as the conceptually simplest example. Starting from the corresponding Yang-Mills Lagrangian, we derive an SU(2) cavity Hamiltonian in the Coulomb gauge, represented in terms of only three localized bosonic modes. Unlike its non-interacting electromagnetic counterpart, this model exhibits a nontrivial excitation spectrum featuring bound composite gauge particles ('glueballs') as the lowest-energy configurations. We extend this framework to one-dimensional arrays of coupled SU(2) cavities and discuss the driven excitation of a glueball condensate and the clustering of multi-glueball states as two elementary interaction-induced processes in these models. These examples offer a glimpse into the multitude of novel many-body phenomena that arise within this cavity SU(2) framework and we show how this physics at the interface between particle physics and quantum optics can be experimentally explored using state-of-the-art superconducting quantum circuits.
Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure SU(3)SU(3)SU(3) lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model H2-2\texttt{H2-2}H2-2, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires ∼25n\sim 25n∼25n entangling gates for nnn Trotter steps.