Validation

Cross-Validation

Two independent simulators confirm the validity of AGE-TGI-2S3/IDS + QEC results

Independent Verification

The scientific validity of any simulation result depends on its reproducibility. To ensure the robustness of our AGE-TGI-2S3/IDS + QEC results, we have developed two independent simulators with different code architectures and verified that they produce numerically consistent results.

The compare_simulators.py script runs both simulators with the same input parameters and compares the outputs metric by metric. The results show agreement within expected numerical precision (differences < 10⁻¹² for double-precision calculations), confirming that the results are not artifacts of a particular implementation.

Simulator 1

Direct 2×2 matrix multiplication

Simulator 2

Euler angle parameterization

The two approaches are algebraically equivalent but numerically distinct, providing robust cross-validation.

Verification Methodology

Cross-validation follows a rigorous protocol. Both simulators receive identical input parameters (operators A and B, time step h, code distance d, detection efficiency ηdet) and independently calculate:

  1. The approximate unitary U_approx via the 7-segment sequence
  2. Gate fidelity F = |Tr(U_target†U_approx)|²/4
  3. Physical error per segment 1 - Feff
  4. Logical error εlogical for the chosen QEC code
  5. GHZ state fidelity for N qubits

Simulator Differences

Simulator 1

Direct 2×2 matrix multiplication

Simulator 2

Euler angle parameterization

Agreement

Comparison Results

Metric Simulator 1 Simulator 2 |Δ| Status
F (h=0.1) 0.999999999847 0.999999999847 < 10-12 ✔OK
1 - Feff 4.762×10-2 4.762×10-2 < 10-12 ✔OK
εlog (d=5, η=0.95) 7.180×10-3 7.180×10-3 < 10-12 ✔OK
εlog (d=13, η=0.95) 1.400×10-6 1.400×10-6 < 10-12 ✔OK
εlog (d=13, η=0.99) ~10-9 ~10-9 < 10-9 ✔OK
FGHZ (N=5, d=13) 0.940 0.940 < 10-12 ✔OK
Conclusion: The two independent simulators produce numerically identical results within floating-point precision (differences < 10⁻⁹). This confirms that the AGE-TGI-2S3/IDS + QEC results are robust and do not depend on implementation details.
Code

Verification Script

The compare_simulators.py script is available on our GitHub repository for any researcher to replicate the verification. The script is written in pure Python (no dependencies beyond NumPy) and generates a complete comparison report in CSV format.

To run the verification, simply clone the repository and execute:

git clone https://github.com/Algebric-Gate-Engine.git
python compare_simulators.py

The script accepts parameters for the platform, detection efficiency, and code distance, allowing verification of any configuration reported on this website.

View on GitHub →

compare_simulators.py

Language
Python 3
Dependencies
NumPy
Output
CSV report
License
MIT