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Onset of thermalization of q-deformed SU(2) Yang–Mills theory on a trapped-ion quantum computer

Tomoya Hayata, Yoshimasa Hidaka, Yuta Kikuchi

Published Feb 5, 2026• 0 citations
Publisher

Abstract

Abstract Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus – together with rapid advances in quantum-computing hardware – has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional q-deformed SU(2)3 Yang–Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of SU(2)3, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement F-moves. In our demonstrations, the quantum circuits execute up to 47 sequential F-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of F-moves.

DOI
10.21203/rs.3.rs-8735770/v1

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Abstract Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus – together with rapid advances in quantum-computing hardware – has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional q-deformed SU(2)3 Yang–Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of SU(2)3, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement F-moves. In our demonstrations, the quantum circuits execute up to 47 sequential F-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of F-moves.
Nonequilibrium dynamics of quantum many-body systems is one of the main targets of quantum simulations. This focus - together with rapid advances in quantum-computing hardware - has driven increasing applications in high-energy physics, particularly in lattice gauge theories. However, most existing experimental demonstrations remain restricted to (1+1)-dimensional and/or abelian gauge theories, such as the Schwinger model and the toric code. It is essential to develop quantum simulations of nonabelian gauge theories in higher dimensions, addressing realistic problems in high-energy physics. To fill the gap, we demonstrate a quantum simulation of thermalization dynamics in a (2+1)-dimensional qqq-deformed SU(2)3\mathrm{SU}(2)_3SU(2)3​ Yang-Mills theory using a trapped-ion quantum computer. By restricting the irreducible representations of the gauge fields to the integer-spin sector of SU(2)3\mathrm{SU}(2)_3SU(2)3​, we obtain a simplified yet nontrivial model described by Fibonacci anyons, which preserves the essential nonabelian fusion structure of the gauge fields. We successfully simulate the real-time dynamics of this model using quantum circuits that explicitly implement FFF-moves. In our demonstrations, the quantum circuits execute up to 47 sequential FFF-moves. We identify idling errors as the dominant error source, which can be effectively mitigated using dynamical decoupling combined with a parallelized implementation of FFF-moves.
We present a quantum simulation of the SU(2) lattice gauge theory in 1+1 dimensions with one flavor of fermions, performed using the trapped-ion Quantinuum System Model H2. This work is based on the loop-string-hadron (LSH) formulation of the gauge theory, and is distinguished by using qubits to represent both bosonic-gauge and fermionic-matter degrees of freedom. Furthermore, we access the j=1j=1j=1 electric-flux sector beyond the jmax⁡=1/2j_{\max}=1/2jmax​=1/2 truncation commonly used in SU(2) quantum simulations. To that end, we digitize an electric-field degree of freedom using a multiqubit register for representing the bosonic quantum number. Our simulation therefore synthesizes several key ingredients relevant to quantum simulations in higher spatial dimensions, in particular explicit local gauge-field degrees of freedom represented here by a multiqubit bosonic register, while relying solely on circuit-construction optimizations that are expected to scale polynomially with lattice size. This work demonstrates that modern quantum hardware is increasingly able to accommodate the features of complicated but physically important lattice gauge theories while successfully reproducing the expected Trotterized dynamics.
We present a quantum simulation strategy for a (1+1)-dimensional SU(2) non-Abelian lattice gauge theory with dynamical matter, a hardcore-gluon Hamiltonian Yang-Mills, tailored to a six-level trapped-ion-qudit quantum processor, as recently experimentally realized [Nat. Phys. 18, 1053 (2022)]. We employ a qudit encoding fulfilling gauge invariance, an SU(2) Gauss’s law. We discuss the experimental feasibility of generalized Mølmer-Sørensen gates used to efficiently simulate the dynamics. We illustrate how a shallow circuit with these resources is sufficient to implement scalable digital quantum simulation of the model. We also numerically show that this model, albeit simple, can dynamically manifest physically relevant properties specific to non-Abelian field theories, such as baryon excitations. Published by the American Physical Society 2024
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.
Matrix models are an important class of systems in string theory and theoretical physics, with applications to random matrix theory, quantum chaos, and black holes. Hamiltonian Monte Carlo simulations and gauge/gravity duality have been used to study these systems at thermal equilibrium, and the bootstrap program has been used to efficiently determine operator expectation values by imposing positivity constraints. However, simulating real-time, non-equilibrium dynamics remains a fundamental challenge. In this work, we present the first digital quantum simulation of a bosonic matrix model, executed on the Quantinuum System Model H2 trapped-ion quantum computer. We focus on an SU(2)\mathrm{SU}(2)SU(2) gauge theory with a quartic potential as it is simple enough to validate against exact classical solutions and yet complex enough to reflect the non-local structure of larger theories. Using the Loschmidt echo as our primary dynamical observable, we systematically decompose simulation errors into three distinct sources: Hilbert space truncation, Trotterization, and hardware noise. We demonstrate a new post-selection scheme that detects and discards gauge-symmetry violations in the Fock basis and show that at small scales it, along with zero-noise extrapolation, can give modest improvements in fidelity. These approaches struggle to scale to larger system sizes in their current implementations, emphasizing the need to move beyond them and to focus on depth reduction through improved compilation and unitary synthesis, and run-time error handling such as additional error suppression, error detection, as well as error correction approaches. This work establishes a foundation for extending digital quantum simulation to more complex matrix models -- revealing that fundamental challenges in qubit resources and circuit depth remain formidable obstacles for scaling to holographically interesting regimes.
Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation. Simulating the real-time dynamics of such strings, including their breaking, remains a major challenge for classical computations and a promising target for quantum simulations. While recent quantum simulation experiments explored string-breaking dynamics in abelian lattice gauge theories, non-abelian theories are qualitatively distinct because gauge fields themselves carry charge. Here, we report the first quantum simulation of genuine non-abelian string-breaking dynamics in a pure SU(222) lattice gauge theory, where gauge-field self-interactions drive string breaking even in the absence of dynamical matter. Our results are obtained on a trapped-ion quantum computer, using native qudit Hilbert spaces to encode truncated gauge fields on a ladder geometry and implement digital Trotter dynamics. We experimentally study unbreakable and breakable strings generated by fundamental and adjoint static charges, respectively. We locally resolve string oscillations and coherent string breaking through the creation of gluonic excitations driven by non-abelian plaquette interactions. Our work establishes hardware-efficient, problem-tailored qudit simulations as a promising route for accessing non-perturbative dynamics relevant to high-energy physics.