The P Gate Is Native: Hardware Confirmation of the Dual-Spinor Merkabit on IBM Quantum: P Gate Discovery, Z₂ Symmetry, Two-Scale Anti-Bunching, and Full Pentachoric Error Detection
We report the first experimental validation of the merkabit dual-spinor architecture across four circuit families on IBM ibm_strasbourg (Eagle r3, 127 qubits), executed 6–7 April 2026. The central discovery is that the merkabit's defining operation — the P gate, applying asymmetric phase to counter-rotating spinors — compiles to two native Rz gates with opposite signs: P(φ) = Rz(+φ) ⊗ Rz(−φ). On IBM Eagle r3, both Rz gates are virtual-Z frame changes requiring zero duration, zero error, and zero additional circuit depth. The P gate is native. Eight independent hardware results confirm the architecture, spanning 2 to 26 qubits: Ouroboros return fidelity ZP-ORF = 0.968, transpiler confirming U₀†U₀ = I at depth 1 π-lock standing wave ⟨ZZ⟩ = +0.44 vs +0.447 ideal (2% agreement, two independent runs) Parity witness ⟨XX⟩ = −0.450, consistent with |Φ⁻⟩-like entanglement at 90° Bloch separation Z₂ chirality symmetry mean error 0.016 across n = 4, 6, 8, 12 — all below readout noise threshold; non-monotonic ⟨ZZ⟩ breathing confirmed as standing-wave signature Two-scale Fano structure (9-qubit triangle): intra-round Fano F ≈ 0.52–0.54, within-τ dispersion σ ≤ 0.004 across 18 hardware rounds at τ ∈ {1, 5, 12} Inter-round coherence ρ ≈ 0.86 on the same triangle cell, confirming the two-scale standing-wave memory signature predicted by Paper 15 Full pentachoric error detection (26-qubit, 7-node Eisenstein cell): detection rate 0.089 (baseline) → 0.988 (injected), a 89.9 pp jump; 28/28 single-gate injections above 97% Centre-node syndrome weight 2× periphery matching Eisenstein lattice coordination; sub-Poissonian Fano on every injection (F_centre = 0.055 ± 0.009, F_periphery ≈ 0.20); Z₂ chirality symmetry confirmed inside the Fano structure Four of seven formal predictions from earlier papers in the series are retired by hardware data: P3 (Z₂ symmetry, mean error 0.016 vs <5% threshold), P4 (centre-node detection rate, 99.3% vs 91% ± 5% predicted, exceeding the upper tolerance by 3.3 pp), rotation-gap flatness, and two-scale Fano separation. Three predictions (P1 Berry phase, P2 quasi-period, P5 DTC robustness) remain pending for a subsequent session. A cross-platform reanalysis of Google Quantum AI's 420-experiment Willow dataset shows the opposite sign on every metric (F = 2.42 super-Poissonian, super-linear burst scaling, positive spatial correlation), consistent with a topology distinction: IBM heavy-hex maps naturally onto the Eisenstein lattice; Willow's square grid does not. No error mitigation, post-selection, or parameter tuning was applied to any primary result. Keywords: merkabit, dual spinor, P gate, quantum error correction, sub-Poissonian statistics, Eisenstein lattice, pentachoric code, IBM Eagle r3, Google Willow, standing wave, π-lock, Z₂ symmetry, Fano factor, Floquet time crystal
We report the first experimental validation of the merkabit dual-spinor architecture across four circuit families on IBM ibm_strasbourg (Eagle r3, 127 qubits), executed 6–7 April 2026. The central discovery is that the merkabit's defining operation — the P gate, applying asymmetric phase to counter-rotating spinors — compiles to two native Rz gates with opposite signs: P(φ) = Rz(+φ) ⊗ Rz(−φ). On IBM Eagle r3, both Rz gates are virtual-Z frame changes requiring zero duration, zero error, and zero additional circuit depth. The P gate is native. Eight independent hardware results confirm the architecture, spanning 2 to 26 qubits: Ouroboros return fidelity ZP-ORF = 0.968, transpiler confirming U₀†U₀ = I at depth 1 π-lock standing wave ⟨ZZ⟩ = +0.44 vs +0.447 ideal (2% agreement, two independent runs) Parity witness ⟨XX⟩ = −0.450, consistent with |Φ⁻⟩-like entanglement at 90° Bloch separation Z₂ chirality symmetry mean error 0.016 across n = 4, 6, 8, 12 — all below readout noise threshold; non-monotonic ⟨ZZ⟩ breathing confirmed as standing-wave signature Two-scale Fano structure (9-qubit triangle): intra-round Fano F ≈ 0.52–0.54, within-τ dispersion σ ≤ 0.004 across 18 hardware rounds at τ ∈ {1, 5, 12} Inter-round coherence ρ ≈ 0.86 on the same triangle cell, confirming the two-scale standing-wave memory signature predicted by Paper 15 Full pentachoric error detection (26-qubit, 7-node Eisenstein cell): detection rate 0.089 (baseline) → 0.988 (injected), a 89.9 pp jump; 28/28 single-gate injections above 97% Centre-node syndrome weight 2× periphery matching Eisenstein lattice coordination; sub-Poissonian Fano on every injection (F_centre = 0.055 ± 0.009, F_periphery ≈ 0.20); Z₂ chirality symmetry confirmed inside the Fano structure Four of seven formal predictions from earlier papers in the series are retired by hardware data: P3 (Z₂ symmetry, mean error 0.016 vs <5% threshold), P4 (centre-node detection rate, 99.3% vs 91% ± 5% predicted, exceeding the upper tolerance by 3.3 pp), rotation-gap flatness, and two-scale Fano separation. Three predictions (P1 Berry phase, P2 quasi-period, P5 DTC robustness) remain pending for a subsequent session. A cross-platform reanalysis of Google Quantum AI's 420-experiment Willow dataset shows the opposite sign on every metric (F = 2.42 super-Poissonian, super-linear burst scaling, positive spatial correlation), consistent with a topology distinction: IBM heavy-hex maps naturally onto the Eisenstein lattice; Willow's square grid does not. No error mitigation, post-selection, or parameter tuning was applied to any primary result. Keywords: merkabit, dual spinor, P gate, quantum error correction, sub-Poissonian statistics, Eisenstein lattice, pentachoric code, IBM Eagle r3, Google Willow, standing wave, π-lock, Z₂ symmetry, Fano factor, Floquet time crystal
The merkabit's sub-Poissonian error statistics are not a property of IBM's heavy-hex topology. They are a geometric effect that follows the P gate — two Z rotations with opposite signs — regardless of the hardware substrate. Three lines of evidence are presented. 1. Cross-architecture hardware validation. All five Appendix N predictions from the Base Paper are confirmed on IBM Eagle r3 (ibm_strasbourg, ibm_brussels) and IBM Heron r2 (ibm_kingston, 156 qubits, different coupling map). The full protocol was run on Strasbourg and Kingston; Brussels confirmed P5 independently. The P2 local minima at n = 13 (0.688 vs 0.709, ideal 0.696) and n = 27 (0.670 vs 0.694, ideal 0.683) show both architectures bracketing the ideal within 2%. The DTC paired/control ratio on Heron r2 (3.43–3.92×) matches or exceeds all Eagle r3 values (3.20–3.58×). P5 (DTC robustness) is confirmed in this paper's cross-architecture session, completing the Appendix N scorecard: five of five predictions retired on hardware within a single week (6–12 April 2026). 2. Corrected Willow interpretation. Paper 24's conclusion that the sub-Poissonian signal is "architecture-specific to heavy-hex" was premature. The Google Willow surface-code data (F = 2.42, super-Poissonian) lacked the P gate entirely; the comparison was paired-IBM vs unpaired-Google, not hex vs square. The signal is absent from circuits without the P-gate asymmetry, regardless of topology. 3. Square-grid topology simulation. A noisy Monte Carlo simulation comparing hexagonal and square grids under the pentachoric ouroboros cycle shows that at syndrome extraction depth τ ≥ 5, the square grid produces sub-Poissonian Fano factors — and at matched sizes, is more sub-Poissonian than hex at every error rate. The 4×4 square grid (16 nodes) achieves F = 0.285 at ε = 0.10, the tightest anti-bunching of any cell tested. Pre-registered prediction for Google Willow hardware (timestamped before any Google hardware access): Fano factor (2-qubit, τ = 5): F ≈ 0.3–0.7 DTC paired/control ratio: > 3× P1b sign flip: n = 6 → 8 P2 local minimum (n = 13): P ≈ 0.696 P2 quasi-period peak: n = 39 ± 2 Fano (4×4 square grid, τ = 5): F ≈ 0.29 Cirq implementations (P1b, P2, P5) compile to depth 2 on Google hardware via PhXZ gate merging. Total resource: ~200 circuits at 4,096 shots, less than one hour of QPU time. Appendix N scorecard (complete): P1 Berry phase — Confirmed (Paper 25) P2 Quasi-period — Confirmed (Paper 25) P3 Z₂ chirality symmetry — Confirmed (Paper 24) P4 Centre-node detection rate — Confirmed (Paper 24) P5 DTC robustness — Confirmed (this paper, 3 backends, 2 architectures) No error mitigation was applied to any hardware result. All results are from raw hardware counts. No prediction has been missed or revised after the fact. This is Paper 26 of the Merkabit research series.
This paper reports three hardware measurements on IBM ibm_strasbourg (Eagle r3, 127 qubits) on 9 April 2026, confirming two further predictions from the merkabit architecture's Appendix N protocol and completing the rotation gap sweep. Combined with Paper 24, four of the five pre-registered, parameter-free predictions are now retired on quantum hardware. P1 — Berry phase (confirmed): Ramsey interferometry on the dual-spinor pair (zero CX gates, transpiled depth 6) traces Berry phase accumulation across n = 1–12 ouroboros steps. The forward–reversed chirality difference shows the predicted sign flip at n = 6 → 8, peaks at n = 10 (96.4% fidelity vs ideal), and returns to near-zero at n = 12 (cycle closure). Z₂ antisymmetry holds at every step count (max residual 0.048). At n = 4 the hardware matches the ideal to 99.8%. P2 — Quasi-period (confirmed): Stroboscopic return probability P(|00⟩) across n = 1–59 ouroboros steps (30 circuits, single batched IBM job, zero CX gates, depth 6) oscillates at 96–99% fidelity with no visible decay envelope. The predicted quasi-period peak at 3.3T appears at n = 39 = 3.25T (97.9% fidelity), within the ±0.3T tolerance. A secondary peak at n = 57 = 4.75T confirms quasi-periodicity. Tau=5 Fano gap: The 3-merkabit triangle rotation gap (9 qubits, transpiled depth 279, 108 CX/ECR gates) shows the first directional Fano gap: paired F = 0.506 vs control F = 0.564 (gap 0.058 favouring the merkabit). Per-round Fano is stable at 0.487 ± 0.006 across all five syndrome extraction rounds. Appendix N scorecard: P1 Berry phase: sign flip, peak, cycle closure — Confirmed (this paper) P2 Quasi-period 3.3T ± 0.3T — Confirmed at 3.25T (this paper) P3 Z₂ chirality symmetry < 5% — Confirmed at 0.016 (Paper 24) P4 Centre-node detection rate 91% ± 5% — Confirmed at 99.3% (Paper 24) P5 DTC robustness under 10% gate noise — Pending All P1 and P2 circuits are pure single-qubit rotations that transpile to depth 6 regardless of the number of ouroboros steps. They test the E₆ Coxeter angle table, not hardware coherence. No error mitigation was applied. All results are derived from raw hardware counts. This is Paper 25 of the Merkabit research series. Four of five parameter-free predictions were retired on IBM hardware within a single week of quantum processor access (6–9 April 2026), with no prediction missed or revised after the fact. Repository: github.com/SelinaAliens/merkabit_hardware_test — all scripts, raw JSON counts, and IBM job identifiers. Keywords: merkabit, Berry phase, Ramsey interferometry, quasi-period, discrete time quasi-crystal, Fano factor, sub-Poissonian statistics, IBM Eagle r3, pentachoric code, dual spinor, E6 geometry, ouroboros cycle, Coxeter number, zero free parameters, quantum error correction, ibm_strasbourg, Standing wave
Syndrome extraction in superconducting quantum error correction often reports super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap is ΔF = −0.058 ± 0.017 with 95% CI [−0.098, −0.031] (parametric bootstrap synthesising shot-level data from recorded edge fire rates, since raw shot counts are not preserved in the IBM Runtime JSON; B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴). The per-round Fano is the protocol observable (F_round ∈ [0.49, 0.65] across four sessions, paired and control alike); the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository across three SHAs — 5bbfdb6f (2026-04-12), 745f653f (2026-04-15), and 30984cab (2026-04-19) — all before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent, and topology-agnostic in the deep-Floquet regime of the supporting Monte Carlo; hardware execution on Willow is the outstanding test. Scripts and data: https://doi.org/10.5281/zenodo.19663025. This paper consolidates and extends results from Papers 24, 25, and 26 of the Merkabit Research Series.
Syndrome extraction in superconducting quantum error correction often reports super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap is ΔF = −0.058 ± 0.017 with 95% CI [−0.098, −0.031] (parametric bootstrap synthesising shot-level data from recorded edge fire rates, since raw shot counts are not preserved in the IBM Runtime JSON; B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴). The per-round Fano is the protocol observable (F_round ∈ [0.49, 0.65] across four sessions, paired and control alike); the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository across three SHAs — 5bbfdb6f (2026-04-12), 745f653f (2026-04-15), and 30984cab (2026-04-19) — all before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent, and topology-agnostic in the deep-Floquet regime of the supporting Monte Carlo; hardware execution on Willow is the outstanding test. Scripts and data: https://doi.org/10.5281/zenodo.19663025. This paper consolidates and extends results from Papers 24, 25, and 26 of the Merkabit Research Series.
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.
Syndrome extraction in superconducting quantum error correction typically produces super-Poissonian count statistics on both hexagonal (IBM heavy-hex) and grid (Google Willow) architectures. A recent analysis of 756 IBM Eagle r3 experiments found the opposite: sub-Poissonian anti-bunching with Fano factor F = 0.856, distance-independent and with linear rather than super-linear burst scaling. We show that this signal is a property of a specific two-qubit operation — the P gate, defined as P(φ) = R_z(+φ) ⊗ R_z(−φ) — and not of the hardware on which it runs. On IBM Eagle r3 and Heron r2 the P gate compiles to two virtual-Z frame changes at transpiled depth 6 (zero duration, zero gate error); on Google Willow it compiles to a single PhXZ gate per qubit at transpiled depth 2, independent of the number of Floquet steps. On a 9-qubit triangle cell on ibm_strasbourg, paired circuits containing the P gate at matched transpiled depth (279) and two-qubit gate count (108 CX/ECR) return Fano F = 0.506 versus F = 0.564 for the unpaired control — a directional signature that cannot be attributed to decoherence because the two circuits differ only in the presence of the P gate. The aggregate Fano gap of ΔF = −0.058 has a 95% CI of [−0.090, −0.025] (parametric bootstrap, B = 10 000; z = 3.4, p ≈ 6 × 10⁻⁴), excluding zero. The per-round signature is the protocol observable; the aggregate gap is inflated by session-dependent round-to-round correlation (full forensics in the paper). Cross-architecture replication on ibm_kingston (Heron r2, different coupling map) reproduces the paired/control DTC 2T-subharmonic ratio at 3.43–3.92×, matching or exceeding the Eagle r3 range of 3.20–3.58×. A matched-protocol Monte Carlo of the same Floquet cycle on hexagonal and square grids shows that at τ ≥ 5 the square grid produces sub-Poissonian Fano factors as tight as F = 0.370 ± 0.026 (mean ± std across 30 PRNG seeds, 20 000 shots each) on a 4×4 cell — tighter than any hexagonal cell tested up to a 19-node r = 2 Eisenstein lattice. We pre-register eight falsifiable observables for a paired-phase Google Willow run (~1 QPU-hour, ~200 Cirq circuits at depth 2), with a timestamped PREDICTION.md committed to a public repository (SHAs 5bbfdb6f on 2026-04-12 and 745f653f on 2026-04-15) before any Google hardware access. The eight predictions are quantitative and falsifiable; a Willow run inside the predicted ranges confirms platform-independence of the P-gate signature, while a result outside any threshold falsifies the corresponding component of the central claim. The sub-Poissonian signature is gate-dependent and topology-agnostic; hardware execution on Willow is the outstanding test. Scrips and data avilable: DOI: https://doi.org/10.5281/zenodo.19663025This is a combination paper created for submission and peer review based on Paper 24, 25 and 26.