We report the first hardware-executed quantum-classical coordination pipeline on NISQ hardware for a societal coordination problem task-to-member matching in a 500-agent community economy. The three-stage architecture (AI decomposition → 19 qubit quantum semantic scoring on IBM Heron R2 classical QUBO assignment) executes end-to-end on three Heron R2 processors (ibm_fez,ibm_marrakesh, ibm_kingston). We observe a three-tier regret stratification: (i) a noiseless ceiling at 1.48% (five independent simulator controls + ibm_marrakesh), (ii) a classical-kernel tier at 0.86% via the Shin–Teo–Jeong (2024) dequantization kernel K_c, and (iii) a hardware tier at 0.61% reproduced independently on ibm_fez and ibm_kingston with identical θ. Since K_c's RKHS provably contains the quantum kernel's RKHS at logical depth, the hardware tier is a reproducible operating regime outside the dequantized function class. A companion multi-cycle society-model experiment shows pipeline weight choice is a time-horizon-dependent policy decision; the QUBO matcher also acts as a performative Granovetter machine (80% more weak ties than greedy, p = 9.1 × 10⁻⁵, d ≈ 27 at n = 10 runs).
We report the first hardware-executed quantum-classical coordination pipeline on NISQ hardware for a societal coordination problem task-to-member matching in a 500-agent community economy. The three-stage architecture (AI decomposition → 19 qubit quantum semantic scoring on IBM Heron R2 classical QUBO assignment) executes end-to-end on three Heron R2 processors (ibm_fez,ibm_marrakesh, ibm_kingston). We observe a three-tier regret stratification: (i) a noiseless ceiling at 1.48% (five independent simulator controls + ibm_marrakesh), (ii) a classical-kernel tier at 0.86% via the Shin–Teo–Jeong (2024) dequantization kernel K_c, and (iii) a hardware tier at 0.61% reproduced independently on ibm_fez and ibm_kingston with identical θ. Since K_c's RKHS provably contains the quantum kernel's RKHS at logical depth, the hardware tier is a reproducible operating regime outside the dequantized function class. A companion multi-cycle society-model experiment shows pipeline weight choice is a time-horizon-dependent policy decision; the QUBO matcher also acts as a performative Granovetter machine (80% more weak ties than greedy, p = 9.1 × 10⁻⁵, d ≈ 27 at n = 10 runs).
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)
We settle the long-standing open question of whether parameterized quantum circuits can learn high-dimensional semantic relationships on NISQ hardware and whether quantum phenomena provide measurable advantages. Using IBM's 156-qubit Eagle processor ibm_fez, we show that previous limitations of quantum natural language processing were not fundamental but originated from poor encoding design. All headline results below are obtained on real hardware (no error mitigation, free-tier access, November 2025). Key hardware-validated findings: • Encoding hierarchy: 132× performance gap between faithful Direct Angle Encoding (r = 0.989) and destructive Difference Encoding (r = 0.007) • Genuine quantum learning: +1.61 training effect on hardware, transforming actively anti-correlated random unitaries (r = −0.92) into semantically meaningful manifolds (r = +0.69) with only 21 parameters • Entanglement is required: entangled circuits achieve r = +0.69 while product-state ablation collapses to constant output (r = −0.11), yielding +0.81 entanglement advantage on real hardware • Hardware outperforms simulation: +18% correlation improvement versus noiseless simulator • First empirical scaling law for quantum semantic learning: increasing training data from 12 → 40 pairs improves generalization 4.25× (r = 0.08 → 0.34), projecting parity with classical cosine baseline (r ≈ 0.86) at ~100 training examples We establish three architectural prerequisites for quantum semantic learning on NISQ devices: (1) Sparse Encoding, (2) Ancilla-Based Measurement, and (3) Non-Aliased Angle Scaling [0.1, π−0.1]. This record contains: • Complete manuscript (PDF) • All source code (Qiskit 2.2.3) • Trained parameters (best_theta) • Raw IBM Quantum hardware results (JSON) • Publication-ready figures • 83-pair test set and interactive visualizations All experiments are fully reproducible with an IBM Quantum free-tier account. Related software: https://doi.org/10.5281/zenodo.17728126
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.
Abstract This paper reports the first end-to-end fault-tolerant quantum computing stack to clear all four strict-FTQC requirements simultaneously on commodity superconducting NISQ silicon, rented through standard IBM Quantum cloud subscription with no purpose-built research machine, no custom decoder, and no magic-state distillation factory. The four requirements: (i) surface-code quantum error correction at distance d≥3 with logical-error rate below the unencoded baseline; (ii) a universal Clifford+T gate set executed via magic-state injection, with no arbitrary angle physical rotation carrying non-Clifford content on the wire (the algorithm-determined non-Clifford angle never fires on the silicon; the native RZ(θphys) on Heron fires only at Clifford-multiple angles required to compose H, S, T); (iii) heterogeneous primitive composition (teleportation, lattice-surgery CNOT, T-gate, logical memory) on a persistent encoded register; and (iv) runtime admissibility verification on every committed result. All five chips, five chemistry workloads spanning four molecules, and twenty-two governed runs in this paper were executed on the same primitive engine without architectural change. The architectural shift that makes this work on today’s hardware is the d=1 inversion: a 150-qubit governed encoded register held at substrate distance d=1 on the chip’s physical qubits, with logical fidelity preserved by Seed IQ execution governance over the encoded layer rather than by a larger code distance. Where the standard surface-code paradigm grows physical d quadratically to drive the logical-error rate down—and pays for it with magic-state fidelity that degrades as gate depth scales—Seed IQ governance acts as an operational substitute for code distance: it delivers the equivalent error-rate reduction in software while leaving the per-gate channel fidelity available for T-gate injection and Clifford operations intact. The result: the four strict-FTQC requirements hold simultaneously at approximately one physical qubit per logical qubit, against the ∼ 625 physical qubits per logical qubit required by the IBM 2029 roadmap target of d=25 surface code at comparable logical fidelity. Seed IQ is an Active Inference and Adaptive Multiagent Autonomous Control (AMAC) platform from AIX Global Innovations. Campaign summary. Eight stages, April through June 2026, across five IBM Heron processors (r2: IBM Fez, IBM Kingston, IBM Marrakesh, IBM Pittsburgh; r3: IBM Boston). April 9 — surface-code QEC: −88.5% LER reduction at d=3 on IBM Fez, −93.1% at d=5 where the MWPM+UF baseline collapsed, −60.9% at d=3 on 1.28°ø dirtier IBM Pittsburgh silicon. April 23–25 — all four universal FTQC primitives cleared the classical 2/3 entanglement bound at F≈0.99. April 25–26 — heterogeneous TELE→CNOT→T→CNOT→TELE°ø2 composition: 22,500 circuits at Fgoverned=1.0000, zero detected logical errors. May 7–9 — H2, 10 runs across 3 chips, 10/10 inside chem-acc, best ΔE=+0.0157mHa, two chips bit-identical to twelve decimals. May 23 —LiH, 3 runs across 3 chips, 3/3 inside chem-acc, two chips tied at ΔE=+0.056mHa. May 28–30 — H2O, 3 runs across 3 chips, 3/3 inside chem-acc at ΔE=+0.051mHa, all three bit-identical to twelve decimals. May 30–31 — BeH2 equilibrium, 3 runs across 2 chips, 3/3 inside chem-acc at ΔE=+0.000595mHa (2690.9°ø inside, the only sub-wavenumber QPU chemistry commit on record), all three bit-identical to twelve decimals. June 1 — BeH2 transition state (|cHF |2≈0.5 strong multireference, the canonical territory where single-reference CCSD breaks), 3 runs across two Heron processor generations at two Newton optimization depths on the rank-5 C2v trial-state subspace, 3/3 inside chem-acc on a 62-Pauli-term Hamiltonian; the two 2-D Newton runs (IBM Boston Heron r3, IBM Kingston Heron r2) commit bit-identical to twelve decimals at ΔE=+0.018189mHa, and the 4-D Newton run commits at the deeper fixed point at ΔE=+0.012643mHa (126.6°ø inside chem-acc, 1.6°ø inside the CCSD(T) gold band). Aggregate: twenty-two runs, 22/22 inside chemical accuracy. No prior NISQ-chemistry or partial-FTQC-chemistry result on commodity hardware has cleared this combination of accuracy and cross-chip reproducibility. Full per-stage detail in Åò4–Åò12.8. Compliance. All twenty-two committed chemistry runs and every primitive composition stage passed the four-requirement FTQC compliance check: closed Clifford+T compilation, magicstate-injected T-gates, encoded-register fidelity preservation, runtime admissibility verification. Fgoverned=1.0000 is the runtime admissibility pass-rate—every committed primitive cleared every admissibility check across the composition pipeline (22,500 composed circuits per run, replicated across two independent calibration windows for 45,000 circuits total) and the twenty-two chemistry runs, with zero detected logical errors, computed from per-shot stabilizer-syndrome statistics, entanglement-witness measurements, and the three-stage admissibility check under live IBM Heron hardware noise (Åò7, Åò13.13). The twelve-decimal cross-chip identity is the engineered signature of Seed IQ’s admissibility-and-projection contract: the three-stage envelope is designed so that noisy QPU measurement vectors from materially different chips identify the same Newton fixed point on the trial-state subspace; the committed energy is then the Hamiltonian sum E=Pi ci⟨Pi⟩ at that shared fixed point evaluated directly from each chip’s own QPU shot record by direct bitstring counting at the continuous coordinate—no binning, no precomputed energy curve, no offline lookup. IEEE 754 doubles are just the number format the energies are reported in; what makes the twelve decimal places physically meaningful is that materially different chips, with materially different noise, agree at all twelve. That agreement is the operational evidence the envelope is delivering what it was engineered to: an admissibility-and-projection contract that maps independent noisy QPU measurement vectors to the same fixed point on the trial-state subspace (Åò13.10, Åò14).
This paper presents an empirical evaluation of the Qube Engine, a hybrid quantum-classical Variational Quantum Regressor (VQR) implemented on Noisy Intermediate-Scale Quantum (NISQ) systems. The framework integrates classical data encoding via single-qubit rotations, parameterized RY+RZ variational layers, and linear entangling circuits evaluated on 4-qubit quantum registers. Optimization is conducted using classical algorithms (COBYLA) targeting Pauli-Z expectation values and Mean Squared Error (MSE) loss on continuous feature spaces. We evaluate model performance across ideal statevector simulation (AerSimulator) and physical IBM Quantum superconducting processors (ibm_marrakesh, ibm_fez, ibm_kingston). Experimental results demonstrate consistent optimization dynamics and low simulation-to-hardware expectation drift (Δ=0.0188), corresponding to a 98.23% cross-backend output stability score under shallow circuit depths. This work provides a realistic analysis of variational regression dynamics, hardware execution variance, and structural trade-offs for near-term quantum machine learning models on NISQ hardware.