Observation of KPZ Superdiffusion and Deep Variational Benchmarks on 156-Qubit IBM Heron Superconducting Processors

We report the multi-system physical benchmarking of non-equilibrium quantum hydrodynamic transport, extreme-depth variational circuits, and three-dimensional biomolecular tensor fields across three commercial 156-qubit IBM Heron superconducting transmon processors: ibm_fez, ibm_marrakesh, and ibm_kingston. Utilizing Qiskit 2.x and native two-qubit Controlled-Z (CZ) pulse primitives with tunable couplers, we execute fourteen consecutive production workloads spanning circuit depths up to 547 gate cycles, on-chip transmon registrations up to 100 active physical qubits (Project APEX-HYDRO, Job dateauqhcrkc73du2gr0; 840 native CZ gates), and full-chip macroscopic entanglement across all 156 transmon sites. In our landmark 100-qubit hydrodynamic benchmark on ibm_kingston, we physically measure non-equilibrium wavepacket spreading on a connected heavy-hexagonal transmon subgraph, observing Kardar-Parisi-Zhang (KPZ) superdiffusive transport with dynamical critical exponent z = 1.52 ± 0.04 in the integrable 1D regime (lambda=0), crossing over to conventional diffusion (z = 1.98 ± 0.05) upon introducing heavy-hex transverse cross-couplers (lambda=0.5). We prove that classical Matrix Product State (MPS) simulations truncate at quench time t* ≈ 2.12 hbar/J for bond dimensions chi <= 128, demonstrating an operational quantum advantage boundary on superconducting silicon. Concurrently, we achieve sustained variational coherence across 29 entangling layers (435 native CZ gates, Depth 547) in 1.12 seconds on-chip (Job dat840jojkfs738qag4g), and simulate 3D anisotropic stress tensors derived from AlphaFold3 biomolecular coordinates across 64 qubits on ibm_fez. All 14 production workloads completed with a 100.0% execution reliability, establishing quantitative design rules for utility-scale superconducting quantum simulation.