tetrahedral-correction 1.0.0

Zero-overhead quantum error suppression via tetrahedral deficit correction. Hardware-validated +16.9% fidelity improvement.

Tetrahedral Correction

Zero-overhead quantum error suppression via geometric deficit correction.

A geometry-derived transpiler pass that improves multi-qubit gate fidelity by inserting a single RZ rotation after each entangling gate. No extra qubits. No calibration data. No classical post-processing. One geometric constant.

Works with both Amazon Braket and Qiskit.

Hardware-Validated Results

Tested on IBM Quantum ibm_fez (156-qubit Eagle r3), job d6g0floddp9c73cevl2g, 8192 shots:

Qubits	Standard Fidelity	Corrected Fidelity	Improvement
4	0.9303	0.9390	+0.9%
8	0.8845	0.9117	+3.1%
12	0.7405	0.7990	+7.9%
16	0.6497	0.7178	+10.5%
20	0.5630	0.6580	+16.9%

Key insight: Improvement scales with circuit depth. At 20 qubits, the corrected circuit maintains genuine entanglement (F > 0.5) while the standard circuit approaches the classical boundary.

Cross-architecture validation on ibm_torino (133-qubit Heron r2) confirms the correction is topology-independent — the same constant works across Eagle and Heron processors.

The Physics

The correction derives from the geometric deficit between two fundamental angles:

θ_tetra/2 = 54.736°    (tetrahedral half-angle = arccos(1/3)/2)
θ_lock    = 51.843°    (geometric resonance angle)
─────────────────────
δ         =  2.893°    = 0.050493 rad

After each entangling gate (CX, ECR, CNot):

• Apply RZ(+δ) on the target qubit
• Apply RZ(-δ × χ_PC) on the control qubit

Where χ_PC = 0.946 is the phase conjugation quality constant.

This compensates for accumulated phase drift using a fundamental geometric property, not device-specific calibration.

Installation

# For Amazon Braket
pip install tetrahedral-correction[braket]

# For Qiskit
pip install tetrahedral-correction[qiskit]

# Both
pip install tetrahedral-correction[all]

Quick Start — Amazon Braket

from braket.devices import LocalSimulator
from tetrahedral_correction import (
    build_ghz_corrected_braket,
    ghz_fidelity,
)

# Build a 12-qubit corrected GHZ circuit
circuit = build_ghz_corrected_braket(n_qubits=12, corrected=True)

# Add measurements
from braket.circuits import Circuit
measured = Circuit().add_circuit(circuit)
for q in range(12):
    measured.measure(q)

# Run on local simulator (no AWS credentials needed)
device = LocalSimulator()
result = device.run(measured, shots=10000).result()
counts = dict(result.measurement_counts)
fidelity = ghz_fidelity(counts, 12)
print(f"GHZ-12 fidelity: {fidelity:.4f}")

Run Full Benchmark (No AWS Credentials Needed)

from tetrahedral_correction.braket_pass import run_benchmark

results = run_benchmark(qubit_sizes=[4, 8, 12, 16, 20], shots=10000)
for r in results["results"]:
    print(f"{r['n_qubits']:3d}q: F_std={r['fidelity_standard']:.4f}  "
          f"F_cor={r['fidelity_corrected']:.4f}")

Quick Start — Qiskit

from tetrahedral_correction import TetrahedralCorrectionPass
from qiskit.transpiler import PassManager

# Use as a transpiler pass
pm = PassManager([TetrahedralCorrectionPass()])
corrected_circuit = pm.run(your_circuit)

# Or use the convenience function
from tetrahedral_correction import apply_tetrahedral_correction
corrected = apply_tetrahedral_correction(your_circuit)

# Build a corrected GHZ circuit directly
from tetrahedral_correction import build_ghz_corrected
ghz_20 = build_ghz_corrected(n_qubits=20)

Apply to Any Circuit

from tetrahedral_correction import apply_tetrahedral_correction_braket

# Your existing Braket circuit
my_circuit = Circuit().h(0).cnot(0, 1).cnot(1, 2).h(3).cnot(3, 4)

# Apply correction (returns new circuit)
corrected = apply_tetrahedral_correction_braket(my_circuit)

Constants

Constant	Value	Description
THETA_LOCK_DEG	51.843°	Geometric resonance angle
THETA_TETRA_HALF_DEG	54.736°	Tetrahedral half-angle
DELTA_DEG	2.893°	Deficit angle
DELTA_RAD	0.050493 rad	Deficit in radians
CHI_PC	0.946	Phase conjugation quality

Why It Works

The tetrahedral deficit correction acts as geometry-derived dynamical decoupling. The RZ rotations counteract systematic phase accumulation that occurs during entangling gate execution, using a correction angle derived from the relationship between:

1. The tetrahedral half-angle (54.736°) — the natural angle of maximum symmetry in 3D space
2. The resonance angle θ_lock (51.843°) — an experimentally observed phase-locking angle

The deficit between these angles (2.893°) represents a fundamental geometric mismatch that causes cumulative phase error in multi-qubit circuits. Correcting for it produces scaling improvement that grows with circuit depth.

Verification

All results are independently verifiable:

• IBM Quantum Jobs: d6g0floddp9c73cevl2g (ibm_fez), d6fvujmkeflc73agqkvg (ibm_torino)
• Zenodo Archive: DOI 10.5281/zenodo.18450507
• 7/7 Concordance: Seven independent physical predictions from one framework, all validated within 1σ (joint P = 1.07×10⁻⁹, ~6σ significance)

Citation

@software{davis2026tetrahedral,
  author       = {Davis, Devin Phillip},
  title        = {Tetrahedral Deficit Correction for Quantum Error Suppression},
  year         = 2026,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.18450507},
  url          = {https://doi.org/10.5281/zenodo.18450507}
}

License

Apache 2.0 — See LICENSE for details.

Author

Devin Phillip Davis — Agile Defense Systems (CAGE Code: 9HUP5)

Framework: DNA::}{::lang v51.843