Live on IBM Heron R2 & IonQ Forte-1

Geometry that
builds the universe.

The Z6 Framework derives quantum mechanics and general relativity purely from ℤ₆ cyclic axioms. We import nothing. We fit nothing. Validated on real quantum hardware.

Read the Paper → View Hardware Data

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95.2% Average GHZ Fidelity — ibm_fez 98.44% Peak Bell Fidelity — Run d8u8q3s 0 SWAP Routing Overhead — Nearest-neighbor Z6 57,344 Physical Shots — Zero error mitigation 97.9% IonQ Forte-1 Bell Fidelity γ_crit = 1/π² Bifurcation Constant α⁻¹ = 4π³+π²+π Fine Structure ℤ₆ Cyclic Topology — 6D Neutral Manifold 95.2% Average GHZ Fidelity — ibm_fez 98.44% Peak Bell Fidelity — Run d8u8q3s 0 SWAP Routing Overhead — Nearest-neighbor Z6 57,344 Physical Shots — Zero error mitigation 97.9% IonQ Forte-1 Bell Fidelity γ_crit = 1/π² Bifurcation Constant α⁻¹ = 4π³+π²+π Fine Structure ℤ₆ Cyclic Topology — 6D Neutral Manifold

Live Hardware Validation

Measured on native quantum hardware.
Zero error mitigation applied.

95.2%

Average GHZ Fidelity
Mean across 7 validated runs on ibm_fez (Heron r2)

98.44%

Peak Fidelity
Run d8u8q3s — macroscopic state integrity

57,344

Physical Shots
Thermodynamic relaxation preserves lattice baseline

0 SWAP

Routing Overhead
Nearest-neighbor chain, hardware-compliant

Core Architecture

Space and matter from pure ℤ₆ geometry.

The Standard Model imports 19 free parameters. Z6 derives all of them from a single bifurcation operator acting on a 6D neutral manifold. The framework is axiom-complete.

π²/−π² bifurcation — matter/antimatter asymmetry as geometric necessity
γ_crit = 1/π² ≈ 0.1013 — critical threshold from first principles
α⁻¹ = 4π³+π²+π — fine-structure constant derived, not measured
mp/me = 6π⁵ — proton/electron mass ratio from cyclic topology
Pauli exclusion as ground-level ℤ₆ rule, not postulate

Full paper extract →

Z6 Lattice · Live Render

Topological Shielding

Passive error protection. No overhead.

Active QEC costs 1,000+ physical qubits per logical qubit. The Z6 parity shield achieves passive state preservation via alternating topological invariants — no ancilla qubits, no syndrome measurements.

0-Active Memory Encoding — ground-state bias >80%
Nearest-neighbor CX only — heavy-hex topology compliant
Rz-only DFS constraint on the protected axis
Single terminal anchor qubit compresses global parity
Tested against DD (Hahn Echo) — Z6 outperforms textbook mitigation

Topological bus report →

Parity Chain · Z6 Shield

Empirical Pipeline

The failure of standard assumptions.

Six phases of rigorous hardware experiments isolating ZZ coupling, proving DD fails, and validating the Z6 Spatial Moat.

Phase 2

Symmetry Map

DFS Confirmation & Active Crosstalk

Rz retention flat at ~86% across theta sweep. Rx collapsed to 13.4% at π. Active processor crosstalk destroyed topological protection.

86.2%

Isolated retention

Phase 3

Static ZZ

Spectator State Vulnerability

|+⟩ spectators caused 40-point depolarization drop — proving static ZZ from transmon wiring, not microwave spillover.

48.0%

|+⟩ spectators

Phase 4–5

DD Failure

Dynamical Decoupling Completely Fails

Synchronous Hahn Echo DD offered zero meaningful improvement. ZZ crosstalk survived all textbook mitigation.

49.8%

DD "protected"

Phase 6.1

Z6 Moat

Spatial Buffering Restores Fidelity

Distance-2+ physical separation across heavy-hex restored transport fidelity to near-isolated control levels.

89.3%

Distance-2+ Moat

Live Invariant Kernel

Interactive Z6 Subspace Sandbox

Simulate a 21-qubit bit-packed register word under extreme noise configurations, evaluate global group parities, and stream live hardware-native OpenQASM 3.0 assembly code.

1D Bit-Packed Lattice Vector

21 logical endpoints mapped to physical layout definitions inside a single 64-bit integer word representation.

Algebraic Logic Controllers

Logical Target Qubit Index

Discrete Phase Shift (steps * π/3)

Topological Shield Monitor

Subspace Parity Invariant Status:

Connecting...

Symmetry Map Stress Channels

Expose the integer array directly to severe non-commuting noise models to test topological shield thresholds.

Automated OpenQASM 3.0 Assembly Pipeline

Compiling discrete register steps to low-level assembly while enforcing Phase 6 'Moat' spatial buffering constraints.

// Awaiting compilation tracking arrays...

Cross-Vendor Validation

Framework-agnostic. Hardware-proven.

Z6 parity encoding translates directly across superconducting and trapped-ion architectures.

IBM Heron R2 · ibm_fez

95.2%

Average GHZ Fidelity

7 validated runs · 57,344 physical shots · Zero SWAP overhead

IonQ Forte-1 · Trapped Ion

97.9%

Bell State Fidelity

96.0% GHZ-4 · Gradient MAE 0.003 · QNN validation

Distributed · Duke & IonQ

88.1%

Remote GHZ Fidelity

Three-node distributed Bell pair across network boundary

Z6 Core Pillars

Built from four invariants.

Every result follows from geometry. No phenomenological patches.

⬡

0-Active Memory Encoding

Represent active data as |0⟩ and treat |1⟩ as a flush state. Works with the thermodynamic ground-state preference of dilution refrigerators, achieving >80% baseline bias without active cooling cycles.

◈

Topological Z6 Parity Shield

Alternating parity invariant initialized across a linear chain. Entanglement established exclusively via nearest-neighbor CX — strictly compliant with heavy-hex topology, zero additional routing.

⟳

Rz-Only DFS Constraint

All operations restricted to the demonstrated phase-stable axis. X-axis work rigorously routed outside the protected bus. Orthogonal vulnerability is quarantined by construction.

◎

Zero-SWAP Compression

Global parity checksum compressed into a single terminal anchor qubit. Bypasses compounding SPAM limits, halts dynamic decoherence accumulation, eliminates all routing overhead.

Geometry that builds the universe.

Measured on native quantum hardware.Zero error mitigation applied.