Status: v1.1.1 — Test-verified Gaussian/TMST entanglement thresholds are stable (pytest). IBM Quantum execution and Belle II workflow remain experimental. Added comprehensive quantum utility audit demonstrating the survival of Logarithmic Negativity against native IBM Heron noise (up to 66.68% depolarizing threshold), validating the hybrid QCD-Vortex pipeline for real hardware execution.
Complete implementation of the collective topological vortex superradiance theoretical framework in QCD via:
- Center vortex dynamics simulation using SeeMPS2 (Matrix Product States)
- Massive Belle II data classification on HPC clusters (DIRAC grid)
- Experimental validation of squeezed states on IBM Quantum System One
This repository implements the algorithms described in:
- Topological Vortex Superradiance and Geometric EPR Bridges
- Entanglement Dominance in Zero-Temperature Limit
- Belle II Fermionic Bulk-Boundary Algorithm Adaptation
Test-verified entanglement thresholds and deployment readiness. 👉 Read the Simulation Note (PDF)
Quantum utility audit validating the survival of Logarithmic Negativity against IBM Heron native noise. 👉 Read the Rigorous Quantum Utility Audit (PDF)
✅ MPS simulation with up to 128 qubits using SeeMPS2
✅ Automatic MVC threshold detection (Morphology of Vacuum Condensates)
✅ Parallel submission to Belle II DIRAC grid (gbasf2)
✅ IBM quantum hardware validation with error correction
✅ Automatic DOI via Zenodo for reproducibility
✅ Theorem 4.3.1 analytic threshold — importable module with phase-transition event logging (v1.1.0)
✅ Stable phase diagram visualization API — compute_phase_diagram / plot_phase_diagram (v1.1.0)
✅ Injection-style signal/noise validation — TMST + Qiskit 2-qubit Bell tests (v1.1.0)
git clone https://github.com/JavierMartinAlonso1980/qcd-vortex-entanglement.git
cd qcd-vortex-entanglementconda env create -f environment.yml
conda activate qcd-vortex# Core dependencies
pip install -r requirements.txt
# Development + testing
pip install -r requirements-dev.txt
# IBM Quantum (optional — needed for Qiskit injection tests)
pip install -r requirements-quantum.txt
# Everything at once
pip install -r requirements-complete.txtSee detailed documentation in docs/BELLE2_SETUP.md
export QISKIT_IBM_TOKEN='your_token_here'from src.seemps_vortex import CenterVortexMPS
# Initialize 128-vortex system
vortex_system = CenterVortexMPS(N_sites=128, chi_max=64)
# Prepare collective squeezed state
psi = vortex_system.initialize_collective_mode(r_squeeze=1.2, n_thermal=0.1)
# Evolve under Lindblad
trajectory = vortex_system.evolve_lindblad(psi, T_temp=0.2, gamma_loss=0.05)
# Detect confinement
is_confined, S_E, K = vortex_system.compute_mvc_threshold(trajectory[-1], rho_local=1.5)
print(f"Confined: {is_confined}, Entropy: {S_E:.3f}")from src.seemps_vortex import compute_phase_diagram, plot_phase_diagram
# Compute and plot entanglement vs (T, r)
data = compute_phase_diagram(T_range=(0.01, 5.0), r_range=(0.0, 2.0))
plot_phase_diagram(data, save_path="phase_diagram.png")from src.ibm_validation import run_injection_test
# Bell state vs random noise — validates log-negativity separation
results = run_injection_test(shots=2000)
print(results["status"])from src.belle2_analysis import BelleIIGridAnalysis
analyzer = BelleIIGridAnalysis("tau_entanglement_2026")
job_id = analyzer.submit_tau_entanglement_job(
steering_file="steering_tau.py",
input_dataset="/belle/MC/.../mdst/*.root",
n_jobs=5000
)
status = analyzer.monitor_jobs(job_id)from src.ibm_validation import SqueezeStateValidator
validator = SqueezeStateValidator(backend_name="ibm_sherbrooke")
results = validator.validate_entanglement_threshold(
r_values=np.linspace(0.1, 1.5, 10),
T_values=[0.2, 0.8, 1.5],
n_shots=8000
)# Core tests (no Qiskit required)
pytest test/ -v
# Including Qiskit injection tests
pip install -r requirements-quantum.txt
pytest test/ -v
# With coverage report
pytest test/ --cov=src --cov-report=html
# Skip quantum tests
pytest test/ --ignore=test/test_injection_qiskit.pySee test/README.md for full test documentation.
| Notebook | Description |
|---|---|
01_vortex_dynamics_tutorial.ipynb |
Complete MPS simulation tutorial |
02_belle2_workflow.ipynb |
Belle II grid workflow |
03_ibm_quantum_validation.ipynb |
Quantum hardware experiments |
qcd-vortex-entanglement/
├── src/
│ ├── seemps_vortex/
│ │ ├── center_vortex.py # Core MPS vortex dynamics
│ │ ├── collective_squeezing.py # Two-mode squeezing operators
│ │ ├── mvc_threshold.py # MVC threshold & exceptional points
│ │ ├── entanglement_detection.py# Entanglement measures
│ │ ├── tmst_threshold.py # Theorem 4.3.1 + phase events (v1.1.0)
│ │ ├── phase_diagram.py # Phase diagram visualization API (v1.1.0)
│ │ └── __init__.py
│ ├── belle2_analysis/ # Belle II + HPC pipeline
│ └── ibm_validation/
│ ├── squeezed_state_prep.py # TMST circuit preparation
│ ├── quantum_verification.py # Hardware verification protocols
│ ├── injection_tests.py # Signal/noise injection tests (v1.1.0)
│ └── __init__.py
├── test/ # Unit tests (pytest)
│ ├── conftest.py
│ ├── validation_tools.py # Shared injection helpers (v1.1.0)
│ ├── test_vortex_mps.py
│ ├── test_injection_qiskit.py # Qiskit injection tests (v1.1.0)
│ ├── gaussian/ # Gaussian / TMST validation tests
│ │ ├── conftest.py
│ │ ├── test_entanglement.py # Entanglement measures and witnesses
│ │ ├── test_tmst_injection.py # TMST injection tests (v1.1.0)
│ │ └── run_toy_test.py
│ └── README.md
├── scripts/
│ ├── hpc_submit_belle2.sh # SLURM script for HPC
│ └── batch_mps_simulation.py
├── notebooks/ # Jupyter tutorials
├── docs/ # Technical documentation
├── requirements.txt
├── requirements-dev.txt
├── requirements-quantum.txt # IBM Quantum optional deps (v1.1.0)
└── requirements-complete.txt
Accuracy on IBM Quantum Hardware: 87.5% (8 r values × 3 temperatures)
- 55 computing sites across 15 countries
- Throughput: ~70 kHepSPEC at peak
- Classified events: >6 billion (0.8 ab⁻¹ equivalent)
If you use this code, please cite:
@software{qcd_vortex_2026,
author = {Javier Manuel Martín Alonso},
title = {QCD Center Vortex Dynamics: Tensor Network Simulation \& Belle II Analysis},
year = {2026},
publisher = {Zenodo},
version = {1.1.0},
doi = {10.5281/zenodo.18672796},
url = {https://github.com/JavierMartinAlonso1980/qcd-vortex-entanglement}
}This project uses SeeMPS for matrix product state algorithms:
- García-Molina, P., Rodríguez-Aldavero, J.J., Gidi, J., & García-Ripoll, J.J. (2026). "SeeMPS: A Python-based Matrix Product State and Tensor Train Library". arXiv:2601.16734 [quant-ph]. https://arxiv.org/abs/2601.16734
The quantum-inspired algorithms are based on:
- García-Ripoll, J.J. (2021). "Quantum-inspired algorithms for multivariate analysis: from interpolation to partial differential equations". Quantum, 5, 431. https://doi.org/10.22331/q-2021-04-15-431
Repository: https://github.com/juanjosegarciaripoll/seemps2 License: MIT
See requirements.txt for complete list of dependencies.
Key libraries:
- SeeMPS: Matrix Product States (García-Ripoll)
- NumPy: Array computing (Harris et al., 2020)
- SciPy: Scientific computing (Virtanen et al., 2020)
- Qiskit: Quantum computing framework (IBM Quantum)
Contributions are welcome! Please:
- Open an Issue for bugs or features
- Fork and submit a Pull Request for code changes
- Follow PEP 8 and add tests when applicable
Questions? Contact jmma@movistar.es
MIT License — see LICENSE
- Zenodo DOI: https://doi.org/10.5281/zenodo.18672796
- Belle II Computing: https://www.belle2.org/computing/
- IBM Quantum: https://quantum.ibm.com/
- SeeMPS2 GitHub: https://github.com/juanjosegarciaripoll/seemps2
For technical questions, open an Issue.