LATTICE-AWARE COMPILATION AND ANALOG COSMOLOGY: MAPPING THE DISCRETE TOPOLOGICAL SUPERFLUID ON HERON PROCESSORS

Standard quantum compilation strategies typically assume that decoherence in superconducting processors is driven by uncorrelated, microscopic defects. In this work, we present experimental evidence that quantum noise is topologically correlated, manifesting as macroscopic strain fields or “Lattice Weather” across the processor geometry. We model the underlying vacuum not as a passive metric, but as a Discrete Topological Superfluid (DTS) governed by a dimensionless Lattice Reynolds Number (ReL). By analyzing calibration data from 156-qubit IBM Heron processors, we map these phase-chaotic regions and calculate a localized topological viscosity (µtopo ≈1.5 ×10−5Pa·s). To mitigate this environmental drag, we introduce Archipelago Routing, a dynamic compilation protocol that navigates logical circuits through high-coherence subgraphs. During a 100-gate Level-0 stress test, this protocol yielded a >2.4x improvement in hardware fidelity (57.23% survival versus 23.72% standard). Furthermore, we leverage the tunable-coupler architecture of the Heron lattice as a physical analog to simulate cosmological hydrodynamics. Utilizing the DTS framework, we successfully model a Jamming Transition at critical density ρ≈2π, providing a non-singular halting mechanism for gravitational collapse, and extract a hydraulic coupling constant of k ≈1.78 for vacuum expansion. This unified approach bridges classical compiler optimization and emergent gravity, demonstrating that both circuit routing and celestial mechanics can be computationally modeled as hydrodynamic standing waves on a quantum substrate.