AbstractWe present Quantum-6502, a self-calibrating BIOS layer for Entanglement-Enhanced Dynamical Tracking (EEDT) based phase-storage on IBM Heron r2 superconducting processors. EEDT is a proof-of-concept phase-storage protocol that demonstrates how always-on ZZ coupling can be converted into a feedforward resource via mid-circuit measurement (MCM), rather than suppressed. Key Features of Quantum-6502 BIOS:Universal Pair Discovery (Layer 0): Automatically discovers suitable qubit pairs from backend calibration data using zero quantum jobs.Ultra-Light Calibration (ULC): Measures νZZ and T2 using only 2 jobs (9 circuits).Adaptive Execution: Executes QFEED+ adaptive feedforward to compensate for per-session drift without user intervention. Hardware Validation Results:Static vs. Dynamic Contrast: On ibm_kingston (Q149+Q150), the system yielded GPS_dynamic = +0.345 ± 0.007 versus GPS_static = −0.201 (Δ = +0.546, z = 47.96σ), assuming shot-level independence with binomial standard error. This contrast provides strong direct evidence consistent with the stochastic collapse-timing mechanism of EEDT.Cross-Backend Consistency: Validation on ibm_marrakesh confirms GPS = +0.037 (z = 8.5σ combined, 8 Holm-corrected conditions) and GPS = +0.726 (z = 66σ).Expanded Operating Regime: The kingston result extends the confirmed operating regime to ωZZT2 = 21.9. Based on the data, τ*/TMCM ≥ 5 is tentatively proposed as the operative constraint, ensuring that measurement overhead remains subdominant to coherent evolution.Robustness: Sensitivity analysis confirms that EEDT gain remains positive (GPS > 0) across a ±30% variance (covering observed drift ranges) from the MANUAL calibration estimate of νZZ. Consistency with AUTO-mode estimates (where available) indicates no systematic bias introduced by the MANUAL override. AvailabilityThe present validation is restricted to IBM Heron r2. All system code, raw experimental data, and IBM Quantum job IDs are publicly available in the linked repository.
AbstractWe present Quantum-6502, a self-calibrating BIOS layer for Entanglement-Enhanced Dynamical Tracking (EEDT) based phase-storage on IBM Heron r2 superconducting processors. EEDT is a proof-of-concept phase-storage protocol that demonstrates how always-on ZZ coupling can be converted into a feedforward resource via mid-circuit measurement (MCM), rather than suppressed. Key Features of Quantum-6502 BIOS:Universal Pair Discovery (Layer 0): Automatically discovers suitable qubit pairs from backend calibration data using zero quantum jobs.Ultra-Light Calibration (ULC): Measures νZZ and T2 using only 2 jobs (9 circuits).Adaptive Execution: Executes QFEED+ adaptive feedforward to compensate for per-session drift without user intervention. Hardware Validation Results:Static vs. Dynamic Contrast: On ibm_kingston (Q149+Q150), the system yielded GPS_dynamic = +0.345 ± 0.007 versus GPS_static = −0.201 (Δ = +0.546, z = 47.96σ), assuming shot-level independence with binomial standard error. This contrast provides strong direct evidence consistent with the stochastic collapse-timing mechanism of EEDT.Cross-Backend Consistency: Validation on ibm_marrakesh confirms GPS = +0.037 (z = 8.5σ combined, 8 Holm-corrected conditions) and GPS = +0.726 (z = 66σ).Expanded Operating Regime: The kingston result extends the confirmed operating regime to ωZZT2 = 21.9. Based on the data, τ*/TMCM ≥ 5 is tentatively proposed as the operative constraint, ensuring that measurement overhead remains subdominant to coherent evolution.Robustness: Sensitivity analysis confirms that EEDT gain remains positive (GPS > 0) across a ±30% variance (covering observed drift ranges) from the MANUAL calibration estimate of νZZ. Consistency with AUTO-mode estimates (where available) indicates no systematic bias introduced by the MANUAL override. AvailabilityThe present validation is restricted to IBM Heron r2. All system code, raw experimental data, and IBM Quantum job IDs are publicly available in the linked repository.
Noisy Intermediate-Scale Quantum (NISQ) devices suffer from calibration drift—slow, coherent phase errors accumulating between active corrections. We present EEDT (Entanglement-Enhanced Dynamical Tracking), a measurement-gated quantum error correction protocol utilizing noisy measurements to dictate intervention timing. Initial Lindblad simulations yielded a counterintuitive 339% deviation from theoretical bounds, which we identify as the Golden Eye collapse in low-noise regimes (σ_ro < 3%). This motivates a bifurcated theoretical model incorporating Golden Eye Occupancy (high-σ) and noise-floor saturation (low-σ) regimes, achieving 78% prediction accuracy improvement over prior models, with the critical threshold σ_c ≈ 2% analytically derived. New in v8: We report the first statistically significant real-hardware demonstration on three IBM Heron devices (ibm_fez, ibm_torino, ibm_marrakesh). After systematic qubit selection (ε_01 = 1.18%) and direct ZZ Ramsey measurement (ν_ZZ = 0.13 kHz), the stroboscopic CDQEM protocol achieves a correction gain of +0.112 at N_meas = 8 with 2.7σ significance on ibm_marrakesh, confirming the MCM post-selection effect predicted by the stroboscopic convergence theorem. All code, data, and IBM Quantum job IDs are publicly available.
Integrated journal paper introducing the Quantum-6502 framework for self-stabilizing qubit storage units. Implements the EEDT (Entanglement-Enhanced Dynamical Tracking) protocol on IBM Heron r2 (ibm_marrakesh, Q94-Q95). Key results: G_PS = +0.037 ± 0.011, z_combined = +8.8σ across 9 conditions. Operating window τ* ∈ [30,50] µs, N* ∈ [1,5]. Three-pillar noise budget analysis (Aer-hardware gap, storage-gate separation, platform boundary scan) converges on non-Markovian ancilla dynamics. Includes Python code and all figures. v2 (2026-03-07): Quantum-6502 framework, Figure 5, full noise budget, journal paper format.v1 (2026-03-03): Hardware operating conditions report.
We derive analytically that the optimal feedforward phase for ZZ-coupling correction in superconducting qubits is given by the argument of the first circular moment of the accumulated phase distribution: φ* = arctan(S/C), where C = ⟨cos φ⟩ and S = ⟨sin φ⟩. A negative second derivative proves this is always a maximum. We measure GPS = P_ff − P_ref on IBM Heron r2 processors (ibm_kingston, ibm_marrakesh; five qubit pairs) and IQM Garnet (Crystal 20). A robust empirical invariant is observed: π ν_ZZ τ* ≈ const ≈ 0.873 rad, confirmed across five independent IBM configurations (π ν_ZZ τ* = 0.873 ± 0.001 rad). A preliminary τ-scan on IQM Garnet shows a GPS sign reversal consistent with a zero-crossing near φ = 0.873 rad. The result establishes a robust empirical invariant within superconducting architectures, enabling feedforward calibration without full phase tomography. Related work:- EEDT Protocol: https://doi.org/10.5281/zenodo.19029431- Bell Decay Clock: https://doi.org/10.5281/zenodo.19367565- Software (Quantum-6502): https://doi.org/10.5281/zenodo.19160835
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)
Phase accumulation during idle intervals in superconducting qubits is well known, and virtual Z (Rz) gates are routinely used for correction. However, the distinction between unconditional (static) and conditional (timing-aware) phase correction has received limited experimental attention. Here we present experimental results on IBM Quantum superconducting processors showing that unconditional phase correction can systematically degrade fidelity in timing-misaligned regimes, specifically for Bell-type superposition under ZZ-dominated evolution. On ibm_kingston (Heron r2), unconditional correction yields GPS = -0.201 ± 0.007 (z = -27.9σ) while conditional MCM feedforward achieves GPS = +0.345 ± 0.007 (z = +47.96σ), a gap of ΔGPS = +0.546. GPS = F_ff - F_ref isolates the incremental effect of correction by removing baseline decoherence. This result does not invalidate static phase correction globally; the effect emerges only under timing-misaligned stochastic phase regimes. The physical mechanism is derived from H = ξ_ZZ|11⟩⟨11|: applying Rz(-φ*) unconditionally to one qubit of a Bell pair adds φ* to the relative phase rather than canceling it, doubling the phase error at τ*. Density matrix simulation with Kraus operators confirms GPS_static = -0.39 (model). These results demonstrate that phase correction effectiveness is strongly regime-dependent, and identify conditional phase correction as a synchronization primitive between stochastic phase evolution and control application. AI assistance (Claude, Anthropic) disclosed.Data: IBM Quantum Cloud, 2026-03-22, job d6vqgtov5rlc73f5a7kg.Code: https://github.com/okudat9/Quantum-6502
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)