Trapped-ion Quantum Computer Demonstrates (2+1)-Dimensional Yang-Mills Thermalization Dynamics

Scientists are now simulating the complex, nonequilibrium dynamics of quantum field theories, a crucial step towards understanding high-energy physics! Tomoya Hayata (Keio University School of Medicine, RIKEN iTHEMS, and The University of Tokyo), Yoshimasa Hidaka (Yukawa Institute for Theoretical Physics, Kyoto University), and Yuta Kikuchi (Quantinuum K.K.) et al. have achieved a significant breakthrough by demonstrating the thermalization dynamics of a (2+1)-dimensional q-deformed Yang-Mills theory on a trapped-ion quantum computer! This work extends simulations beyond simpler abelian models, tackling a nonabelian gauge theory and paving the way for investigations into more realistic, high-energy phenomena , a feat previously hampered by computational limitations! Their innovative approach, utilising Fibonacci anyons and explicitly implementing ‘-moves’ in quantum circuits, represents a vital advance in applying quantum computing to fundamental problems in particle physics.

The team overcame limitations of previous studies, which were largely restricted to (1+1)-dimensional or abelian gauge theories, by constructing a simplified yet nontrivial model based on Fibonacci anyons, preserving the essential nonabelian fusion structure of gauge fields. This innovative approach allows for the exploration of genuinely nonabelian dynamics, a significant step forward in the field. The study employed a trapped-ion computer to simulate real-time dynamics using quantum circuits explicitly designed to implement F-moves, local unitary transformations acting on string networks. These circuits executed up to 47 sequential F-moves, enabling the observation of thermalization processes within the q-deformed Yang-Mills theory. Researchers meticulously restricted the irreducible representations of the gauge fields to the integer-spin sector of SU(2), creating a model that, while simplified, accurately reflects the complex behaviour of nonabelian gauge theories. This careful construction was vital for achieving a tractable simulation while retaining the key physical properties of the system. Experiments revealed that idling errors, arising from qubits waiting for operations, were the dominant source of error in the simulation. To combat this, the team implemented a combination of dynamical decoupling and a parallelized implementation of F-moves, effectively mitigating the impact of these errors and improving the accuracy of the results. This demonstrates a crucial strategy for leveraging noisy intermediate-scale quantum (NISQ) devices for complex simulations. The successful execution of 47 sequential F-moves represents a significant technical achievement, pushing the boundaries of what is currently possible with trapped-ion quantum computing. This work opens exciting possibilities for exploring nonperturbative effects in quantum field theories, which are notoriously difficult to compute using classical methods. By simulating the thermalization dynamics of this nonabelian gauge theory, scientists gain valuable insights into the behaviour of fundamental forces and the evolution of the universe. The demonstrated techniques for error mitigation and parallelization are broadly applicable to other quantum simulations, paving the way for more accurate and complex studies of quantum many-body systems and high-energy physics phenomena.

Fibonacci Anyon Simulation of Yang-Mills Thermalisation reveals novel Scientists pioneered a digital quantum simulation of thermalization dynamics within a (2+1)-dimensional deformed Yang-Mills theory, utilising a trapped-ion computer! To overcome limitations in simulating nonabelian gauge theories, the research team restricted irreducible representations of the gauge fields to the integer-spin sector of, creating a simplified model governed by Fibonacci anyons, preserving essential nonabelian fusion structures. This innovative approach enabled the simulation of real-time dynamics via circuits explicitly implementing -moves, achieving up to 47 sequential -moves in their demonstrations! The study meticulously engineered quantum circuits to represent the lattice gauge theory, employing a Trotterized decomposition to approximate the time evolution operator. These circuits were specifically designed to enact -moves, local unitary transformations acting on string networks representing Wilson lines, and were executed on a trapped-ion quantum computer. Researchers harnessed dynamical decoupling, a technique to mitigate idling errors, identified as the dominant noise source, by applying carefully timed pulses to the qubits, effectively shielding them from environmental noise during the computationally intensive -move sequences. Furthermore, the team implemented a parallelized version of the -moves, significantly enhancing the efficiency of the simulation and reducing the overall circuit depth. Precise measurements of qubit states were performed after each -move to track the evolution of the system, and the resulting data was analysed to verify the correct implementation of the gauge dynamics. This method achieves a crucial balance between circuit complexity and error mitigation, allowing for the observation of nontrivial real-time dynamics in a genuinely nonabelian gauge theory, a feat previously unattainable. The work demonstrates that current noisy quantum devices possess the capability to simulate complex physical systems, provided that circuits are carefully designed and effective error-mitigation strategies are employed. By identifying memory noise as the primary error source and successfully mitigating it with dynamical decoupling, the study paves the way for scaling up quantum simulations of nonabelian lattice gauge theories and exploring regimes inaccessible to classical computation.

Fibonacci Anyons Simulate Yang-Mills Thermalisation Scientists achieved a groundbreaking simulation of thermalization dynamics in a (2+1)-dimensional deformed Yang-Mills theory using a trapped-ion computer! This work successfully demonstrates a pathway towards simulating nonabelian gauge theories in higher dimensions, a significant challenge in high-energy physics. By restricting irreducible representations of the gauge fields to the integer-spin sector, the team obtained a simplified model described by Fibonacci anyons, preserving the essential nonabelian fusion structure crucial for accurate representation. The researchers implemented circuits that explicitly execute -moves, achieving up to 47 sequential -moves in their demonstrations. Experiments revealed that idling errors were the dominant source of error during the simulations, but these were effectively mitigated through the application of dynamical decoupling combined with a parallelized implementation of -moves. Data shows that carefully designed quantum circuits and appropriate error-mitigation techniques are essential for scaling up these experiments and studying nonequilibrium dynamics in classically intractable regimes. Measurements confirm the successful implementation of F-moves, leveraging the strengths of digital quantum computation to accurately model the system’s behaviour.

The team constructed the basis of quantum states using a network of Wilson lines, represented graphically as a network of strings, with the one-plaquette system basis visually depicted as a1 a2 a3 a4 a5 a6 c6 c5 c4 c3 c2 c1. The fusion rule of Wilson lines, a × b = P c Nc abc, governs their interaction, and the researchers focused on Fibonacci anyons, corresponding to the integer-spin sector of the q-deformed SU(2)3 Yang-Mills theory. Tests prove that the local basis satisfying the constraints at a vertex is graphically.

Results demonstrate the successful implementation of the Kogut-Susskind Hamiltonian, HYM = HE + HM, which describes the dynamics of the system. The electric-field operators are represented as E2 i a = δaτ a, and the plaquette operator, tr Uτ a1 a2 a3 a4 a5 a6 c6 c5 c4 c3 c2 c1, is defined using the F-move, [Fciai−1τ a′ i ]aia′i−1. The nontrivial F-move for Fibonacci anyons is [Fτττ τ ] = 1 φ 1 φ 1 2 1 φ 1 2 −1 φ, with φ being the golden ratio, φ = (1 + √ 5)/2. This breakthrough delivers a crucial step towards quantum simulations of nonabelian gauge theories on noisy quantum hardware, paving the way for addressing practical high-energy physics problems with quantum computers. F-moves Simulate Nonabelian Gauge Theory Scientists have demonstrated a digital quantum simulation of a nonabelian lattice gauge theory on a trapped-ion quantum computer! This achievement addresses a significant challenge in high-energy physics, where simulating nonequilibrium dynamics is crucial but computationally demanding. Researchers constructed a simplified model preserving the nonabelian fusion rule of Wilson lines, enabling the real-time evolution of the model with explicit F-moves representing nonabelian anyons. The experiments successfully implemented circuits executing up to 47 sequential F-moves, identifying idling errors as the primary source of error. Mitigation strategies, including dynamical decoupling and parallelized F-moves, proved effective in reducing these errors. The findings highlight that, unlike typical spin-model benchmarks, error budgets in this context are more strongly influenced by memory noise during multi-qubit operations than by the number of entangling gates. Authors acknowledge limitations stemming from circuit depth and suggest future work focusing on aggressive optimization strategies and exploring more complex anyon categories like SU(2)k or SU(3)k. Further research will also involve incorporating dynamical matter fields and scaling up system size, requiring more efficient circuit decompositions and tailored error mitigation techniques to fully harness the potential of quantum computation in this field. 👉 More information 🗞 Onset of thermalization of q-deformed SU(2) Yang-Mills theory on a trapped-ion quantum computer 🧠 ArXiv: https://arxiv.org/abs/2601.13530 Tags: