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.
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.
Experimental measurement data of the QITE formalism (Quantum-Inspired Thermal Equilibrium) on IBM quantum processors of the Heron R2 generation with 156 physical qubits. Altogether 75+ jobs on two different backends (ibm_kingston and ibm_fez), over 830,000 shots, carried out on 8, 10, and 11 April 2026. Seven experiment series: (1) Static phases (R=0.5 / 1.0 / 2.0): three clearly separated Hamming-weight distributions (16.3σ significance), positive ZZ correlations under QITE (+0.318 at R=2.0) versus negative ones in the null experiment (−0.061). Controlled comparison experiment with null hypothesis (identical circuit structure with random parameters). (2) Real-time feedback loop (8 cycles): two targeted perturbations (R=3.0 and R=0.3); the system returns autonomously to equilibrium within 2 cycles. First demonstration of dynamic controllability of a QITE quantum collective on a real quantum computer. (3) Cross-backend reproducibility: identical results on ibm_kingston and ibm_fez — deviations within a few percent. (4) Zero-noise extrapolation (ZNE): circuit folding (1×, 3×, 5×) with Richardson extrapolation. Result: coherence 0.474 → 0.474 extrapolated (improvement: −0.0005). The optimized circuit (depth 13, 120 CZ gates) already operates at the hardware noise floor — ZNE cannot improve it further because the circuit is already near-optimal. (5) Scaling comparison 27 vs. 156 qubits: the 27-qubit version on the same backend (ibm_kingston) shows ZZ correlation of 0.788 against 0.318 at 156 qubits (Δ = +0.470). Circuit depth drops from 13 to 6, CZ gates from 120 to 13. Confirms: the QITE signal scales with gate quality. (6) Extended feedback loop (20 cycles): four extreme perturbations — R=3.0 (excess), R=0.3 (deficit), R=5.0 (5-fold excess), R=0.1 (10-fold deficit). Maximum coherence C=0.785 (highest value ever measured). The system reorganizes itself after each perturbation within 2–4 cycles. Long-term stability demonstrated across 20 cycles and 436 seconds of total runtime. (7) 3-minute stability demonstration (20 cycles, 262.7 seconds): dedicated long-term test with two targeted shocks (R=4.0 and R=0.2). Result: ones_fraction remains between 0.491 and 0.499 over 4.4 minutes (maximum deviation from equilibrium: 0.009). Drift across the entire runtime: +0.003. Complete recovery after both shocks. 18/18 non-shock cycles stable. First demonstration of a self-correcting quantum field on a real quantum computer over several minutes. Circuit optimization relative to 8 April: reduction of circuit depth from 295 to 13 (factor 22×), two-qubit gates from 1,946 to 120, by exclusive use of native Heron R2 gates (CZ, SX, RZ, X) and direct lambda encoding via RY(θ) with θ = 2·arctan(λ₂/λ₁). The system demonstrably produces controllable, correlated, self-organizing quantum states on real hardware — no simulation, no theory, but physical measurement data of a concrete technical system. All 59 IBM job IDs are contained in the raw data and verifiable on quantum.ibm.com. German patent applications Az. 10 2025 003 906.9 (QITE) and Az. 10 2025 004 891.2 (QISE). Final document (12 April 2026) — 21 sections, 9 experiment series, 372 individual quantum measurements. Extensions compared to the previous version: Section 19: 9-minute experiment (209 cycles, 156 qubits, 4096 shots) Phase A: null test (23 cycles, R=1.0) — baseline control measurement Phase B: 8 shocks (R=0.1 to R=8.0) incl. double shock — complete recovery after each shock Section 20: overall summary of all 9 experiment series (8–12 April 2026) Section 21: raw-data appendix with SHA-256 checksums of all 9 JSON files Core results: 372 quantum measurements on IBM Heron R2 (ibm_kingston, ibm_fez) Dynamic range R=0.1 to R=8.0 (factor 80) with complete self-correction The null test proves: recovery is an active process, not a hardware artefact No drift, no collapse across 209 consecutive measurements Optimized circuit: depth 13, 120 CZ gates, at the hardware noise floor (ZNE-confirmed)
On 1 June 2026, a decentralized per-qubit lambda field was implemented on the IBM Heron R2 processor (ibm_kingston, 156 qubits) and probed with a multi-shock excitation protocol. Unlike the predecessor work (Westrick, QITE Hardware Results 156Q, 8-12 April 2026), which tested a globally controlled QITE quantum collective, each qubit here carries its own lambda state and receives, in the feedback loop, only its own measurement statistic p1_i. The only inter-qubit coupling propagates physically through the CZ gates of the Heavy-Hex topology. Six shocks were applied at six different positions on the chip: central (q*=78), nearest neighbor (d=1), intermediate (d=3, d=5), deep (d=8), and edge (d=12). Each individual shock triggered a chip-wide burst within 1-8 cycles (peak |delta p1| between 0.308 and 0.366; 10 to 22 simultaneously active qubits). Four additional spontaneous bursts were detected between shocks, for a total of 10 bursts in 150 cycles. The 6/6 reproducibility was verified by four independent non-parametric statistical tests, all positive: (1) permutation test p = 0.008 against chance alignment; (2) pairwise burst-vector Pearson correlation r_mean = +0.65 with all 15 pairs above noise; (3) cross-session reproducibility 9/10 qubit overlap between two independent IBM Quantum sessions, hypergeometric p = 0.008; (4) Mann-Whitney U test of burst amplitude versus Phase-A baseline, ratio 2.7, p < 0.0001. This bundle contains the complete primary data (raw JSON logs, NumPy matrices), all 27 visualizations, IBM job IDs of every submitted job, console logs of all runs, the pre-registration documents with locked detection thresholds, and SHA-256 checksums of every file (MANIFEST.json) for independent verification. Backend: IBM Heron R2 (ibm_kingston), 156 qubits, 4096 shots/cycle. Patent filings: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE). Predecessor: Westrick, QITE Hardware Results 156Q (8-12 April 2026).
On 4-5 July 2026, an identical shock protocol was executed on the same 156-qubit IBM Heron R2 architecture (ibm_fez) but with the QITE lambda feedback replaced by uniformly random rotation angles per cycle. This random-angle null control preserves every structural variable — RY+RZ+CZ layer, Heavy-Hex CZ coupling, 4096 shots/cycle, seed 20260602, the same 150 cycles, and the same six shocks at the same cycles (20/40/60/80/100/120), the same target qubits (q78, q69, q67, q47, q37, q16) with the same amplitudes (l1,l2) — while removing only the decentralized per-qubit lambda feedback dynamics. Backend selection was driven by queue availability; both are 156-qubit Heron R2 devices with identical architecture, and calibration differences cannot account for the qualitative burst-count contrast reported below. The result is a clean negative: zero collective bursts across all six shocks. The four non-parametric statistical tests (identical methodology to v1) all confirm the absence of shock-driven collective response: (1) permutation test yields p = 1.0 for shock alignment against the noise-saturated per-cycle transitions; (2) pairwise Pearson correlation between per-transition delta-p1 vectors drops from r_mean = +0.65 in the multi-shock run to r_mean = +0.017 in the null; (3) cross-session hypergeometric overlap between null "top-active" qubits and the v1 multi-shock top-active set is not significant (Jaccard = 0.11, p = 0.24); (4) Mann-Whitney U on shock-cycle max|delta p1| versus baseline shows ratio 0.989 with p = 0.89 — statistically indistinguishable from noise. Baseline global coherence exp(-8*Var(p1)) sits at 0.413 +/- 0.022 across all 150 cycles under random angles, versus 0.99 +/- 0.01 under QITE feedback in v1 — two distinct dynamical regimes. That the shock protocol itself executed correctly on the null run is verified locally at the target qubit: for each of the six shocks, the measured p1[q_target] at the shock cycle agrees with the theoretical prediction from theta_shock = 2*atan2(l2, l1) to within <5% (q78 shock: predicted 0.016, measured 0.018; q69 shock: predicted 0.985, measured 0.939; and so on for all six). One cycle after each shock, the target qubit returns to the random baseline distribution — with no feedback dynamics, there is no restoring trajectory. The shocks are physically executed; what is absent is the collective response. Causal conclusion: the QITE per-qubit lambda feedback dynamics are necessary for the observed collective burst phenomenology. The circuit structure (RY+RZ+CZ on Heron R2 Heavy-Hex topology) and shock protocol alone do not produce bursts. Six identical shocks on QITE-stabilized baseline produce 10 collective bursts with 6/10 shock-aligned (p = 0.008); the same six shocks on random baseline produce zero. This 10-vs-0 hardware contrast, verified by four independent non-parametric tests, establishes feedback necessity as a falsifiable causal claim rather than a phenomenological observation. The v2 bundle contains the complete null-control primary data (150-cycle JSONL, consolidated JSON, p1 numpy matrix), all IBM Runtime job IDs with per-cycle timestamps, Tee'd console logs of both the initial run and the resume run (a mid-run job-poll stall on 4 July required a resume from cycle 7 with deterministic per-cycle RNG seeds), five analysis figures including direct null-vs-multi comparison plots, the full side-by-side statistical comparison JSON, the v1 multi-shock p1 matrix and statistical test outputs for reanalysis, an 8-page supplement PDF (Section 5) integrating with the v1 paper, and SHA-256 checksums of every file in MANIFEST_v2.json. Backend (v2 null control): IBM Heron R2 (ibm_fez), 156 qubits, 4096 shots/cycle.Companion patents: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE).Predecessor (v1): Westrick, Reproducible Collective Burst Modes on 156 Qubits: Decentralized Per-Qubit QITE Lambda Field on IBM Heron R2, 1 June 2026. On 1 June 2026, a decentralized per-qubit lambda field was implemented on the IBM Heron R2 processor (ibm_kingston, 156 qubits) and probed with a multi-shock excitation protocol. Unlike the predecessor work (Westrick, Controllable Quantum Collective States on 156 Qubits: Experimental Results of the QITE Formalism on IBM Heron R2, 12 April 2026), which tested a globally controlled QITE quantum collective, each qubit here carries its own lambda state and receives, in the feedback loop, only its own measurement statistic p1_i. The only inter-qubit coupling propagates physically through the CZ gates of the Heavy-Hex topology. Six shocks were applied at six different positions on the chip: central (q*=78), nearest neighbor (d=1), intermediate (d=3, d=5), deep (d=8), and edge (d=12). Each individual shock triggered a chip-wide burst within 1-8 cycles (peak |delta p1| between 0.308 and 0.366; 10 to 22 simultaneously active qubits). Four additional spontaneous bursts were detected between shocks, for a total of 10 bursts in 150 cycles. The 6/6 reproducibility was verified by four independent non-parametric statistical tests, all positive: (1) permutation test p = 0.008 against chance alignment; (2) pairwise burst-vector Pearson correlation r_mean = +0.65 with all 15 pairs above noise; (3) cross-session reproducibility 9/10 qubit overlap between two independent IBM Quantum sessions, hypergeometric p = 0.008; (4) Mann-Whitney U test of burst amplitude versus Phase-A baseline, ratio 2.7, p < 0.0001. This bundle contains the complete primary data (raw JSON logs, NumPy matrices), all 27 visualizations, IBM job IDs of every submitted job, console logs of all runs, the pre-registration documents with locked detection thresholds, and SHA-256 checksums of every file (MANIFEST.json) for independent verification. Backend: IBM Heron R2 (ibm_kingston), 156 qubits, 4096 shots/cycle.Patent filings: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE).Predecessor: Westrick, Controllable Quantum Collective States on 156 Qubits, 12 April 2026.
We report the observation of long-range dynamical protection and coherent transport of two-qubit entangled states across discrete 1D lattice chains on a 156-qubit superconducting quantum processor (ibm_marrakesh). By combining an affine geometric phase gradient with periodic CPMG dynamical decoupling and Hermitian conjugate frame unwinding, we suppress continuous dephasing, spatial wavepacket dispersion, and accumulative cross-resonance errors. The protocol achieves an unmitigated Bell state fidelity of 97.92% +/- 0.10% across 512 physical SWAP gates (1,536 native two-qubit hardware operations) and maintains an unmitigated fidelity of 97.93% +/- 0.22% (Tr(rho^2) = 0.9591) through 1,024 physical SWAPs (3,072 native pulses), contrasting with bare unmitigated transport decay (F < 1%). We demonstrate spatial transport scaling across up to 101 contiguous transmons (89.06% fidelity across 198 SWAPs), confirm the attractor basin geometry under continuous 3D Bloch sphere parameter sweeps (theta in [0, 2pi]), and validate sensitivity to intentional single-qubit phase and bit-flip defect injections.
We report forward random-circuit sampling (RCS) on the 120-qubit Nighthawk r2 superconducting processor (ibm_phoenix) with square-lattice connectivity, using 61 qubits, native CZ gates, and the standard cloud execution stack with no benchmark-specific calibration. Two independent fidelity estimators---mirror benchmarking and three- and four-patch cross-entropy benchmarking (XEB)---agree with each other at every measured depth, the mirror from 4 to 40 cycles and the patched estimators from 20 to 40 cycles, across more than two orders of magnitude of fidelity decay, and exceed the first-generation Nighthawk r1 device by more than an order of magnitude at fixed depth. The 36-cycle circuits sit at the depth where tensor-network contraction cost saturates at system size: a contraction-cost estimator validated against the published Sycamore and Zuchongzhi networks places the single-amplitude cost at ∼1022 complex operations. At FXEB(36)=2.3×10−3 under favorable memory assumptions this implies 1.2×1027 machine operations within the bounded-fidelity rejection-sampling model --- more than a century of runtime on the Frontier supercomputer --- to collect a 106-sample ensemble, which takes only 19\,s on Nighthawk r2. To our knowledge, this is the first demonstration of quantum advantage for a vanilla random-circuit sampling on a commercially and broadly accessible quantum processor that most non-expert quantum computer users can easily replicate.
Eight verified quantum computing jobs executed on IBM Quantum hardware (ibm_fez Heron R2, 156 qubits; ibm_torino Heron R1, 133 qubits) between January 27 and March 15, 2026. User ID: IBMid-692001DJRD. Experiments include: 1. Bell State Entanglement — 96.3% fidelity on ibm_fez Heron R2 (Concurrence C = 0.926, Tangle T = 0.858, 1,000 shots). Cross-platform benchmark: Heron R2 vs Heron R1 (+8.3 pp fidelity advantage, noise ratio 2.43×). 2. Reproducibility Test — Two independent runs of identical circuit (χ² = 2.70, p = 0.44, df = 3). H₀ not rejected: statistically indistinguishable results at 95% confidence. 3. BB84 Quantum Key Distribution — Full Alice/Eve/Bob protocol implementation. Alice baseline error 0.60% → Bob QBER 49.0% under eavesdropping (82× degradation). Experimental demonstration of the quantum no-cloning theorem. Control group design isolates eavesdropper signal from hardware noise baseline. 4. Variational Quantum Circuit (VQC) — 2-qubit circuit, 10 trained parameters with tied weights (θ₃ = θ₄), 8 CZ gates in 4 entangling layers. 4-qubit ansatz: Shannon entropy 3.885/4.000 bits (97.1%), ground-state bias confirmed (χ² = 300.94, p ≈ 0). 5. Quantum Random Number Generation (QRNG) — 8-bit outputs, 10/10 unique values per shot (range 16–254). Total: 39,010 quantum measurements across 8 jobs and 10 circuits. QPU time: 4.8 seconds. Job completion rate: 100%. All results decoded from raw IBM SamplerV2 BitArray binary archives (zlib + base64 + NumPy .npy pipeline). No simulations. Statistical validation applied throughout (Wilson 95% CIs, chi-squared tests). Stack: Qiskit Runtime SamplerV2 · QPY · OpenQASM 2.0 · Python · NumPy · SciPy Repository: https://github.com/dinohatibovicWhitepaper: https://dinohatibovic.github.io (Doc QAI-WP-2026-01-28-V4)