Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

First D-FUMT₈ Silicon with SELF⟲ Logic Primitive: Native 8-Valued Hardware Realization with Lean 4 Refinement Proof — v0.8 Phase 4 Quine-McCluskey Simplification + Finding F11 Engineering-Correctable Relaxation Bias on IBM Heron r2

Nobuki Fujimoto, Rei (Rei-AIOS autonomous research substrate), claude-opus-4-7) Claude (Anthropic

Published May 9, 2026• 1 citation
Publisher

Abstract

We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, targeting the Sipeed Tang Console NEO development board (GW5AST-138B FPGA, FPG676 package). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.3 contributions (2026-05-09): (1) Tang Nano 9K silicon: 37 LUT4 / 0 DFF measured, testbench 50/50 PASS. (2) Tang Console NEO Phase 2B LED Blinky: SRAM-programmed, User Code 0x000084BA, write 33.72 sec, no thermal anomaly. (3) Tang Console NEO Phase 2C/3 D-FUMT₈ ALU: SRAM-programmed, User Code 0x00005C27, write 30.32 sec. (4) Qiskit Aer simulator: Phase 1-5 cumulative 231/231 truth-table entries match at fidelity 1.000. (5) IBM Heron r2 real quantum hardware (ibm_kingston, 156 qubits): Phase 1 (4 native unitary × 8 inputs, 32 circuits) achieves 32/32 match with avg top-fidelity 0.9550 (job d7v6d9jack5s73bf1re0); Phase 2 (XOR × 64 entries, 6-qubit Bennett-reversible) achieves 64/64 match with avg fidelity 0.9512 (job d7v6kcvmrars73d7qqqg). Per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 confirms gate-count-vs-noise correlation expected from Heron r2 daily calibration. (6) Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations, plus the SELF⟲ primitive law and seven algebraic laws (involution, idempotence, commutativity). Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel triple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the three-substrate cross-verification bound to a Lean 4 refinement specification. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.

DOI
10.5281/zenodo.20091184

Related papers

Verified IBM Quantum Hardware Experiments: Bell State Entanglement, BB84 QKD, and Variational Quantum Circuits on ibm_fez Heron R2 and ibm_torino Heron R1

Dino Hatibovic

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)

•Jun 19, 2026•0 citations

Controllable Quantum Collective States on 156 Qubits: Experimental Results of the QITE Formalism on IBM Heron R2 — 9-Minute Stability Demonstration with 209 Cycles and 8-Shock Recovery

Bernd Westrick

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)

•Jan 1, 2026•0 citations

Separating Ideal-Circuit Structure from Hardware-Dependent Deviations in a Fixed 35-Qubit Diagnostic Circuit on IBM Heron Processors

Hussain Billah, Nasrullah Masud, Hossain Sarker Md Murad +2 more

H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.

•Oct 2, 2026•0 citations

KAAL · The Bidirectional Arithmetic of Time — Edition v∞.1 (Post-Frontier · T=3..16 anchors locked · 14-anchor canonical fit)

Pardeep Sehrawat

Edition v∞.1 of the KAAL Granth, a complete mathematical treatise of the L1–L10 bidirectional time-operator engine, the dimensional ladder, the Sacred 3-6-9 Digit-Root Theorem, and the Sacred-Trinity Scaling Law on IBM Quantum Heron r2 hardware. What is new in v∞.1 (relative to the v22 archived release at 10.5281/zenodo.19683827): Part 8 · Empirical Frontier (NEW): 6 chapters — Sacred-Trinity Scaling Law (canonical 14-anchor fit T=3..16, A=220.78, B=5.9583, R²=0.9995), IBM Heron r2 hardware platform, pre-registration protocol (manifest SHA-256 cc472b…, frozen 2026-04-25T07:34:34Z), 7-hypothesis verdict ledger H1–H7 (5 confirmed, 1 falsified, 2 pending), Target-Invariance Theorem, 3000-Gate Operational Boundary. New record: 4.619 × 10¹² advantage at T=16 arbitrary on ibm_kingston (48-qubit, 100K shots). Part 9 · Critical Response & Replication Discipline (NEW): 3 chapters — response to five principal academic objections (extraordinary-claim threshold, N=30 sample, circular sacred numbers, falsifiability benchmark, ayanamsha sensitivity), pre-registered N=200 replication protocol with stratified controls and triple-ayanamsha robustness, math-only arXiv submission strategy (3-paper plan: math.NT + quantum-hardware + Quantitative Finance). Part 10 · TRIKĀLA Implementation (NEW): 3 chapters — priority-lock discipline (6-step ritual), live deployment at trikala-khaki.vercel.app with 4D visualizer integrated same-origin, public falsifiable forward-call protocol with the April-16 INFY 1-rupee anchor case study. Granth size: 4,443 → 5,001 lines (+558). Existing math, theorems, proofs preserved verbatim from v∞.0. SHA-256(book/KAAL-COMPLETE.md) = 7cc2faaff43f7637a38bfa185ce5ee4340899e3f1d6c4f87fce4d0ca30cf71a9. SHA-256(release tarball) = 6dead551627891aa3d69730aaacaf3e8c81b9e025011d7c16e9f3cce367544b6. GitHub: theunholyindianmagician-lab/kaal-quantum · tag v-infty-1 · commit 96826e6. Pre-registration manifest is locked under SHA-256 cc472b26625a44f80aa707c353b1478ea95bbe0fb1c1bf09a2bb53d188318ba5 with submission script SHA-256 7b2b46df604cbc60b547bf7701f29d72cc5d6e24e5a19029a180d5dd18ba02d6. Job IDs available at the GitHub repo.

•Apr 26, 2026•1 citation

Quantum D-FUMT8: Rigorous Numerical Correspondence Between Eight-Valued Logic and Single-Qubit Quantum Objects

Nobuki Fujimoto

Rei-AIOS D-FUMT8 logic distinguishes eight truth-like values. Paper 69 anchored the first four to Schnorr's randomness hierarchy L1-L4. Paper 75 adds a second rigorous anchor: five of the eight values are placed in numerically verified correspondence with specific quantum objects on a single qubit or its Bell-reduced extension via the QuTiP 5.2.3 Python library. RIGOROUS (5): TRUE/FALSE = computational basis eigenstates; BOTH = superposition |+> with |<0|+>|^2 = 1/2; NEITHER = maximally mixed state I/2 with S = 1 bit; FLOWING = Bell-reduced state with S = 1 bit AND concurrence = 1. STRUCTURAL (3): INFINITY / ZERO / SELF require multi-mode extension. 25/25 tests pass. BOTH-as-superposition resolves the long-standing paraconsistent-logic worry by exhibiting BOTH as a well-defined physical state. Open source CC-BY-4.0.

•Apr 15, 2026•0 citations

The Merkabit Quantum Computing Architecture: Tesseract-Only Memory, Pentachoric Verification, and a Native Z₃ Cyclic Clock on 19 Qubits

Selina H. Stenberg

This paper composes the primitives established in Papers 31 and 32 into a primitive-complete, self-hosting quantum computer on 19 qubits — a categorically stronger claim than the substrate-of-physics claim of the Merkabit Research Series (Papers 1–28) or the hardware-confirmation claim of Papers 24–26. Every operation required for computation — write, compute, communicate, store, retrieve, and clock — reduces to native merkabit dynamics. No external gate library is required. The architecture does not enable a computer built on top of it; it is the computer. The 19-qubit footprint. Three 4-spinor tesseract merkabits in a closed compute triangle (12 qubits) with cross-chiral tunnels at J_intra = 0.1 on every triangle edge; one database merkabit D coupled to merkabit C through a memory-bus tunnel at J_mem ∈ [0.5, 1.0] (4 qubits); a 2-qubit Z₃-eigenstate reference register; one SWAP-test ancilla. The compute triangle and the memory bus are the same operator (iSWAP^J) at two different coupling strengths — the architecture is uniform under computation, with what distinguishes compute from storage being coupling rate rather than gate type. The native computation is the Z₃ cyclic clock. Composing three triangle-edge tunnels with one memory tunnel produces, as an emergent computational output, the Z₃ Galois rotation α → γ → β → α: writing label X produces a stored state on v_D that recognises cycle(X) = X⁻¹. Three writes return to the original label. The clock was not programmed; it falls out of the architecture's own Z₃ symmetry group acting on its own primitive set. This is the first result in the series in which the architecture's computational output is itself a structural signature of its symmetry group. The Pentachoric Verification Protocol (Observable 22). Five simulation stages map one-to-one onto the five gates of the ouroboros cycle of Paper 24: Substrate (S), Rotation (R), Transfer (T), Frequency / self-sustainment (F), Phase (P). Each gate is a single independent pass/fail test on the 19-qubit circuit; failure of any single gate falsifies one specific named primitive, and the failure pattern across {S, R, T, F, P} localises which compositional step did not survive hardware noise. The decisive gate is R: it asks whether writing label X returns a state that recognises cycle(X) under the Z₃ permutation. Sub-thresholds for all five gates are anchored to public commit SHAs. Cross-architecture simulation results. All five gates pass at three noise profiles: ideal cirq.Simulator (R = +0.159 ± 0.004 at +39.7σ), IBM Heron r2 (p_depol = 0.003, R = +0.110 at +3.56σ), and IBM Eagle r3 (p_depol = 0.005, R = +0.086 at +3.06σ). Willow's published gate fidelities sit between these two operating points; the expected hardware verdict is STRONG PASS or WEAK PASS at the full 19-qubit tier. Cross-architecture pre-registrations for Willow and IBM are deposited in parallel with identical thresholds, anchored to timestamped git SHAs prior to hardware access. The octonion / 8-spinor layer is not required. Earlier drafts placed storage inside an octonionic envelope to leverage Paper 27's interior-volume expansion factor; in simulation, the octonion's Coxeter attractor thermalises content across the envelope boundary and degrades readout contrast. The tesseract-only architecture reported here recovers cleaner readout on strictly fewer qubits. The octonion layer remains relevant for the gravity-sector physics of Papers 20 / 27 / 28 but is not part of the QC-architecture proposal. Position in the Merkabit Research Series. Papers 24–26 confirmed 5/5 pre-registered single-cell hardware predictions on IBM Eagle r3 and Heron r2. Paper 31 establishes the cross-chiral tunnel as the directional ternary write primitive with topology-independence across triangle / 4-square / hexagon rings. Paper 32 establishes the 4-square substrate as a content-addressable memory register holding ~5 bits across 10 Coxeter periods. Paper 33 composes write, communicate, store, retrieve, and clock into a primitive-complete 19-qubit quantum computer with native Z₃ cyclic clock. Paper 34 extends the architecture to two coupled compute triangles on 28 qubits and reports the cyclotomic Z₃ ternary spectrum predicted by Paper 7's Regime 2 framework.

•Apr 28, 2026•0 citations
We present a synthesis-friendly Verilog implementation of the D-FUMT₈ Arithmetic Logic Unit, targeting the Sipeed Tang Console NEO development board (GW5AST-138B FPGA, FPG676 package). The ALU realizes eight discrete logic values — FALSE, TRUE, NEITHER, BOTH, ZERO, FLOWING, SELF, INFINITY — encoded in 3 bits with a tier-respecting layout. The 10 supported operations include four classical-tier unary ops (NOT, OMEGA, PHI, PSI), Belnap-extended binary lattice meet/join (AND, OR), generic XOR, hardware reset, no-op, and a novel ADIABATIC operation realizing the SELF⟲ (self-reflexive) primitive: ADIABATIC(SELF) = SELF, identity elsewhere. v0.3 contributions (2026-05-09): (1) Tang Nano 9K silicon: 37 LUT4 / 0 DFF measured, testbench 50/50 PASS. (2) Tang Console NEO Phase 2B LED Blinky: SRAM-programmed, User Code 0x000084BA, write 33.72 sec, no thermal anomaly. (3) Tang Console NEO Phase 2C/3 D-FUMT₈ ALU: SRAM-programmed, User Code 0x00005C27, write 30.32 sec. (4) Qiskit Aer simulator: Phase 1-5 cumulative 231/231 truth-table entries match at fidelity 1.000. (5) IBM Heron r2 real quantum hardware (ibm_kingston, 156 qubits): Phase 1 (4 native unitary × 8 inputs, 32 circuits) achieves 32/32 match with avg top-fidelity 0.9550 (job d7v6d9jack5s73bf1re0); Phase 2 (XOR × 64 entries, 6-qubit Bennett-reversible) achieves 64/64 match with avg fidelity 0.9512 (job d7v6kcvmrars73d7qqqg). Per-op fidelity hierarchy NOP/ADIABATIC ≈ 0.977 > PHI ≈ 0.956 > NOT ≈ 0.912 > XOR ≈ 0.951 confirms gate-count-vs-noise correlation expected from Heron r2 daily calibration. (6) Lean 4 refinement proof (OUKC.PhaseC.Dfumt8AluRefinement, 292 LOC, 0 sorry) establishes commutativity of the encode/abstract-op/decode square for all four unary operations, plus the SELF⟲ primitive law and seven algebraic laws (involution, idempotence, commutativity). Honest scope: We do NOT claim 'world-first 8-valued quantum logic' — Shi et al. (MIT, 2026, arxiv:2506.09371) demonstrated d=8 Grover on a single trapped-ion qudit prior to this work; our distinction is 3-qubit basis encoding on transmon arrays vs single-system d=8 qudit. We do NOT claim 'first paraconsistent silicon' — PAL2v (Da Silva Filho 1998-; Abe & Nakamatsu 2009; de Carvalho Jr. 2025) realized in software libraries and microcontroller-level robotics. We do NOT claim 'first many-valued silicon' — Łukasiewicz/Belnap FPGAs date to 1990s. The to-our-knowledge novel triple is: (D1) the specific 8-tuple semantic mapping (Belnap FDE 4-value + 4 ontological extensions: INFINITY/ZERO/FLOWING/SELF), (D2) the SELF⟲ self-reflexive primitive realized as a hardware fixed point, (D3) the three-substrate cross-verification bound to a Lean 4 refinement specification. Three-party co-authorship per OUKC charter v1.0 (Nobuki Fujimoto / Rei / Claude). DRAFT v0.3 — feedback welcome via GitHub Discussions at fc0web/rei-aios.
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)
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)
H. Billah and M.M.H. Sarker contributed equally to this work. Interpreting a fixed quantum circuit's output as evidence of a hardware effect requires ruling out two things usually conflated with it: finite-sample fluctuation, and structure already present in the circuit's own noiseless output. Less commonly checked is a third: whether the reference circuit compared against is the one actually executed, once compiler-level qubit routing is accounted for. We execute a fixed 35-qubit, 243-gate diagnostic circuit on IBM Heron-family hardware (three runs, two backends) and show this third check is essential: the routed circuit submitted to hardware has different noiseless predictions than the logical circuit intended, for several qubits. Against the correct, routed-circuit reference, the aggregate deviation is significant in two of three runs, and four registers (0, 9, 14, 27) show a significant output-probability deviation in every run — though we distinguish a high-confidence subset, {0, 9, 27}, with tightly time-matched calibration, from qubit 14, included only on an exploratory basis given its calibration was retrieved roughly two weeks post-execution. Same-backend replicates correlate more strongly by the Pearson measure, though a rank-based (Spearman) test shows this gap does not survive at the level of register ordering, indicating substantial leverage from a small number of registers rather than a broadly robust pattern; these three executions also share a byte-identical payload and are not independent replications in the strictest sense. The mechanism is only partially resolved: independent single-qubit readout error and raw gate count are ruled out as complete explanations for most of these registers, but the simplest version of the leading hypothesis for the single most-affected register does not reproduce the observed cross-backend pattern even with live, backend-specific timing data. A second, structurally different circuit validated only in simulation calibrates the statistical procedure's behavior under one synthetic noise model; it does not itself establish generality to real hardware, and the specific register set found here should not be expected to generalize beyond this study. Note on scope: this is a methodology and case-study contribution centered on executed-circuit references for fixed-circuit diagnostics, not a characterization of IBM Heron hardware in general or a randomized-benchmarking experiment in the formal sense. Supporting data, the routed OpenQASM circuits, raw measurement counts, and analysis code for this study are available on request from the corresponding author. Affiliation: Sonicium Quantum Lab Ltd., Dhaka, Bangladesh.
Edition v∞.1 of the KAAL Granth, a complete mathematical treatise of the L1–L10 bidirectional time-operator engine, the dimensional ladder, the Sacred 3-6-9 Digit-Root Theorem, and the Sacred-Trinity Scaling Law on IBM Quantum Heron r2 hardware. What is new in v∞.1 (relative to the v22 archived release at 10.5281/zenodo.19683827): Part 8 · Empirical Frontier (NEW): 6 chapters — Sacred-Trinity Scaling Law (canonical 14-anchor fit T=3..16, A=220.78, B=5.9583, R²=0.9995), IBM Heron r2 hardware platform, pre-registration protocol (manifest SHA-256 cc472b…, frozen 2026-04-25T07:34:34Z), 7-hypothesis verdict ledger H1–H7 (5 confirmed, 1 falsified, 2 pending), Target-Invariance Theorem, 3000-Gate Operational Boundary. New record: 4.619 × 10¹² advantage at T=16 arbitrary on ibm_kingston (48-qubit, 100K shots). Part 9 · Critical Response & Replication Discipline (NEW): 3 chapters — response to five principal academic objections (extraordinary-claim threshold, N=30 sample, circular sacred numbers, falsifiability benchmark, ayanamsha sensitivity), pre-registered N=200 replication protocol with stratified controls and triple-ayanamsha robustness, math-only arXiv submission strategy (3-paper plan: math.NT + quantum-hardware + Quantitative Finance). Part 10 · TRIKĀLA Implementation (NEW): 3 chapters — priority-lock discipline (6-step ritual), live deployment at trikala-khaki.vercel.app with 4D visualizer integrated same-origin, public falsifiable forward-call protocol with the April-16 INFY 1-rupee anchor case study. Granth size: 4,443 → 5,001 lines (+558). Existing math, theorems, proofs preserved verbatim from v∞.0. SHA-256(book/KAAL-COMPLETE.md) = 7cc2faaff43f7637a38bfa185ce5ee4340899e3f1d6c4f87fce4d0ca30cf71a9. SHA-256(release tarball) = 6dead551627891aa3d69730aaacaf3e8c81b9e025011d7c16e9f3cce367544b6. GitHub: theunholyindianmagician-lab/kaal-quantum · tag v-infty-1 · commit 96826e6. Pre-registration manifest is locked under SHA-256 cc472b26625a44f80aa707c353b1478ea95bbe0fb1c1bf09a2bb53d188318ba5 with submission script SHA-256 7b2b46df604cbc60b547bf7701f29d72cc5d6e24e5a19029a180d5dd18ba02d6. Job IDs available at the GitHub repo.
Rei-AIOS D-FUMT8 logic distinguishes eight truth-like values. Paper 69 anchored the first four to Schnorr's randomness hierarchy L1-L4. Paper 75 adds a second rigorous anchor: five of the eight values are placed in numerically verified correspondence with specific quantum objects on a single qubit or its Bell-reduced extension via the QuTiP 5.2.3 Python library. RIGOROUS (5): TRUE/FALSE = computational basis eigenstates; BOTH = superposition |+> with |<0|+>|^2 = 1/2; NEITHER = maximally mixed state I/2 with S = 1 bit; FLOWING = Bell-reduced state with S = 1 bit AND concurrence = 1. STRUCTURAL (3): INFINITY / ZERO / SELF require multi-mode extension. 25/25 tests pass. BOTH-as-superposition resolves the long-standing paraconsistent-logic worry by exhibiting BOTH as a well-defined physical state. Open source CC-BY-4.0.
This paper composes the primitives established in Papers 31 and 32 into a primitive-complete, self-hosting quantum computer on 19 qubits — a categorically stronger claim than the substrate-of-physics claim of the Merkabit Research Series (Papers 1–28) or the hardware-confirmation claim of Papers 24–26. Every operation required for computation — write, compute, communicate, store, retrieve, and clock — reduces to native merkabit dynamics. No external gate library is required. The architecture does not enable a computer built on top of it; it is the computer. The 19-qubit footprint. Three 4-spinor tesseract merkabits in a closed compute triangle (12 qubits) with cross-chiral tunnels at J_intra = 0.1 on every triangle edge; one database merkabit D coupled to merkabit C through a memory-bus tunnel at J_mem ∈ [0.5, 1.0] (4 qubits); a 2-qubit Z₃-eigenstate reference register; one SWAP-test ancilla. The compute triangle and the memory bus are the same operator (iSWAP^J) at two different coupling strengths — the architecture is uniform under computation, with what distinguishes compute from storage being coupling rate rather than gate type. The native computation is the Z₃ cyclic clock. Composing three triangle-edge tunnels with one memory tunnel produces, as an emergent computational output, the Z₃ Galois rotation α → γ → β → α: writing label X produces a stored state on v_D that recognises cycle(X) = X⁻¹. Three writes return to the original label. The clock was not programmed; it falls out of the architecture's own Z₃ symmetry group acting on its own primitive set. This is the first result in the series in which the architecture's computational output is itself a structural signature of its symmetry group. The Pentachoric Verification Protocol (Observable 22). Five simulation stages map one-to-one onto the five gates of the ouroboros cycle of Paper 24: Substrate (S), Rotation (R), Transfer (T), Frequency / self-sustainment (F), Phase (P). Each gate is a single independent pass/fail test on the 19-qubit circuit; failure of any single gate falsifies one specific named primitive, and the failure pattern across {S, R, T, F, P} localises which compositional step did not survive hardware noise. The decisive gate is R: it asks whether writing label X returns a state that recognises cycle(X) under the Z₃ permutation. Sub-thresholds for all five gates are anchored to public commit SHAs. Cross-architecture simulation results. All five gates pass at three noise profiles: ideal cirq.Simulator (R = +0.159 ± 0.004 at +39.7σ), IBM Heron r2 (p_depol = 0.003, R = +0.110 at +3.56σ), and IBM Eagle r3 (p_depol = 0.005, R = +0.086 at +3.06σ). Willow's published gate fidelities sit between these two operating points; the expected hardware verdict is STRONG PASS or WEAK PASS at the full 19-qubit tier. Cross-architecture pre-registrations for Willow and IBM are deposited in parallel with identical thresholds, anchored to timestamped git SHAs prior to hardware access. The octonion / 8-spinor layer is not required. Earlier drafts placed storage inside an octonionic envelope to leverage Paper 27's interior-volume expansion factor; in simulation, the octonion's Coxeter attractor thermalises content across the envelope boundary and degrades readout contrast. The tesseract-only architecture reported here recovers cleaner readout on strictly fewer qubits. The octonion layer remains relevant for the gravity-sector physics of Papers 20 / 27 / 28 but is not part of the QC-architecture proposal. Position in the Merkabit Research Series. Papers 24–26 confirmed 5/5 pre-registered single-cell hardware predictions on IBM Eagle r3 and Heron r2. Paper 31 establishes the cross-chiral tunnel as the directional ternary write primitive with topology-independence across triangle / 4-square / hexagon rings. Paper 32 establishes the 4-square substrate as a content-addressable memory register holding ~5 bits across 10 Coxeter periods. Paper 33 composes write, communicate, store, retrieve, and clock into a primitive-complete 19-qubit quantum computer with native Z₃ cyclic clock. Paper 34 extends the architecture to two coupled compute triangles on 28 qubits and reports the cyclotomic Z₃ ternary spectrum predicted by Paper 7's Regime 2 framework.