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

Abstract

Simulating real-time dynamics in lattice gauge theories (LGTs) is severely constrained by the circuit depth overhead of standard fermion-to-qubit mappings, which scale linearly or quadratically with system size. To overcome this depth-scaling bottleneck, we introduce the Hardware-Aware Lattice Optimization (HALO) compiler, an architecture executing global time-evolution in an immutable $\mathcal{O}(1)$ circuit depth per Trotter step. By natively mapping composite gauge links to hardware topologies, HALO achieves a $91.36\%$ reduction in entangling gate overhead compared to unoptimized Jordan-Wigner baselines, compressing a 16-qubit global step to 56 CNOTs and bypassing extensive $\mathcal{O}(N)$ scaling limits. We validate this compiler on IBM superconducting transmon processors by simulating the mesoscopic Quantum Link Model (QLM) truncation of the Schwinger model. Coupling $\mathcal{O}(1)$ compilation with Zero-Noise Extrapolation (ZNE), we track localized string rupture, extracting the dynamical crossover of pair creation at $t \approx 0.790$ with an $18.3 \pm 2.2\%$ rupture probability. Furthermore, we map the dynamical phase diagram, identifying the confinement phase boundary at $g_c = 1.0$. Finally, we introduce a scalable 2D unit-cell blueprint, paving a direct pathway toward the fault-tolerant simulation of two-dimensional Quantum Chromodynamics (QCD).