We expand on recent work arXiv:2601.17199 demonstrating the existence of a novel entanglement radius $\xi_0$ characterizing flux tube entanglement entropy (FTE$^2$) in (2+1)D Yang-Mills theory. This physical scale corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE$^2$. We consider here geometries of the entanglement region $V$ on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as $\xi_0$. Our results further the conclusions of arXiv:2601.17199 by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.

Several hadronic observables are nowadays computed in lattice QCD with a sub-percent precision which requires the inclusion of strong isospin-breaking and electromagnetic effects. Most of the methods that implement the photon propagator in finite-volume lead to power-law suppressed finite-size effects and do not allow for a straightforward crosscheck against phenomenology and other calculations. Both issues can be avoided by working with a Pauli-Villars regulated photon propagator defined directly in the continuum and infinite volume. This methodology can be profitably exploited to improve the determination of leading-order electromagnetic corrections to several observables such as the HVP or nucleon masses. In this work we apply the strategy to the charged/neutral pion mass difference using CLS ensembles.

In quantum computations of gauge theories at finite temperature and finite density, it is challenging to enforce Gauss's law for all states contributing to the thermal ensemble. While various techniques for implementing gauge constraints have been proposed, they often involve practical trade-offs. In this work, we adopt the Quantum Minimally Entangled Typical Thermal States (QMETTS) algorithm for $\mathbb{Z}_2$ gauge-constrained systems, which allows us to capture thermal equilibrium states with chemical potential while mitigating these trade-offs. To ensure that gauge invariance is preserved throughout the procedure while maintaining computational efficiency, we derive the specific measurement bases within the algorithm. Furthermore, since the estimation of expectation values on quantum hardware is inherently noisy, we rigorously account for shot noise in estimating expectation values, and propose a sampling method that is more efficient than those in previous works. We validate our approach numerically by studying a (1+1)-dimensional $\mathbb{Z}_2$ gauge theory coupled to staggered fermions. Our proposed algorithm reproduces the correct equilibrium states at finite temperature and finite density.

The real-time evolution of strongly interacting matter remains a frontier of fundamental physics, as classical simulations are hampered by exponential Hilbert space growth and rapid, unmanageable growth of quantum entanglement. This study reports the quantum simulation of hadron dynamics within a (1 + 1)-dimensional SU(2) lattice gauge theory using a 156-qubit IBM superconducting processor. Leveraging a hardware-efficient Loop-String-Hadron (LSH) encoding, we simulate the dynamics of the physical degrees of freedom on a 60-site lattice in the weak-coupling regime, as a crucial step toward the continuum limit. We successfully observe the light-cone propagation of a confined meson and internal oscillations indicative of early-time hadronic breathing modes. Notably, these high-fidelity results were obtained directly from the quantum data via a differential measurement protocol, together with measurement error mitigation, demonstrating a robust pathway for large-scale simulations even on noisy hardware. To validate the results, we benchmarked the quantum algorithm and its outcomes from the quantum processor against state-of-the-art approximated classical algorithms using tensor network methods and Pauli propagation, respectively. Furthermore, we provide a quantitative comparison demonstrating that as the system approaches the weak-coupling or the continuum limit, the quantum processor maintains a consistent structural robustness where classical tensor networks and Pauli propagation methods encounter an onset of exponential complexity or symmetry violations as an artifact of approximation in the algorithm. These results establish a scalable pathway for simulating non-Abelian dynamics on near-term quantum hardware and mark a critical step toward achieving a practical quantum advantage in high-energy physics.