The HALO Engine: $\mathcal{O}(1)$-Step Compilation and Localized String Rupture for Lattice Gauge Theories on Quantum Hardware

arXiv:2608.19243v1 Announce Type: new Abstract: Simulating the real-time dynamics of lattice gauge theories (LGTs) represents a challenge for near-term quantum computing. Standard digital simulations rely on Trotterization schemes where circuit depth scales proportionally with lattice size, inevitably colliding with the coherence limits of noisy intermediate-scale quantum (NISQ) hardware. To deal with this depth-scaling bottleneck, we introduce the Hardware-Aware Lattice Optimization (HALO) compiler, an architecture that executes global time-evolution steps in an immutable $\mathcal{O}(1)$ circuit depth per Trotter step. Leveraging this framework, we elevate the digital simulation of the Quantum Link Model (QLM) truncation of the Schwinger model to the mesoscopic scale, utilizing a composite multi-qubit gauge link representation to support non-trivial electric field dynamics. We initialize and execute the non-perturbative dynamics of a heavily stretched $L=15$ meson string on a 16-qubit superconducting transmon processor. By coupling the $\mathcal{O}(1)$ compilation with Zero-Noise Extrapolation (ZNE), we suppress physical hardware decoherence to extract the precise dynamical crossover of localized pair creation, identifying the topological transition at $t \approx 0.790$ lattice units with an $18.3 \pm 2.2\%$ rupture probability. Furthermore, we empirically map the dynamical phase diagram of the mesoscopic lattice, pinpointing the effective confinement phase boundary at precisely $g_c = 1.0$. Finally, we extend the mathematical principles of the HALO engine to higher dimensions, presenting a scalable, constant-depth 2D unit-cell blueprint that eliminates the routing overhead of magnetic plaquettes, paving a direct algorithmic pathway toward the fault-tolerant simulation of two-dimensional Quantum Chromodynamics (QCD).