Symmetry-Driven Coherence Restoration — Reference Implementation
A reference implementation for exploring symmetry-selection mechanisms in open quantum systems. This software provides tools to model, compare, and validate SDCR effects within standard open-system quantum dynamics frameworks.
For the complete theoretical foundation, mathematical derivations, and phenomenological predictions, see:
Symmetry-Driven Coherence Restoration: Geometric Phase Control, Open-System Dynamics, and Phenomenological Signatures
Krüger, M., & Feeney, D. (2025).
Symmetry-Driven Coherence Restoration: Geometric Phase Control, Open-System Dynamics, and Phenomenological Signatures.
Zenodo. https://doi.org/10.5281/zenodo.17942413
SDCR is not a new dynamical law.
It is a symmetry-selection mechanism acting on the reduced dynamics of open quantum systems.
Within standard formulations (e.g. Lindblad, Redfield), SDCR operates by:
- Identifying symmetry-aligned operator sectors
- Suppressing decohering channels incompatible with those symmetries
- Inducing small, systematic bounded phase corrections
- Explicitly recovering ordinary decoherence behavior when symmetry alignment is removed
All dynamics remain fully compatible with conventional open-system quantum theory.
This repository provides tools to:
- Define open quantum system dynamics using standard generators (Lindblad-type models)
- Apply explicit symmetry-selection operators Πsym to reduced dynamics
- Compare baseline decoherence against symmetry-aligned evolution
- Extract observable quantities such as:
- coherence decay
- bounded phase offsets
- Demonstrate the recovery limit, where SDCR effects vanish when symmetry alignment is disabled
- Generate explicit null tests suitable for independent verification
The implementation prioritizes clarity, traceability, and falsifiability over performance or optimization.
This project explicitly does not:
- Introduce new particles, interactions, or collapse mechanisms
- Modify the Schrödinger equation or violate global unitarity
- Claim performance improvements, speedups, or technological superiority
- Provide active quantum error correction or feedback control
- Serve as a general-purpose quantum simulator
- Make claims beyond those stated in the associated paper
Any algebraic structures (e.g. quaternionic or octonionic bookkeeping) are used strictly as internal organizational tools and are never interpreted as physical degrees of freedom.
The repository is organized to clearly separate executable SDCR logic, validated visualizations, illustrative figures, and supporting artifacts.
sdcr-core/
│
├── core/
│ ├── dynamics.py # Open-system generators (Lindblad)
│ ├── symmetry.py # Symmetry selectors Π_sym
│ ├── recovery.py # Recovery / null-limit logic
│ ├── observables.py # Coherence and phase extraction
│ └── utils.py # Shared helpers and validation
│
├── algebra/
│ ├── quaternionic.py # Internal bookkeeping (non-physical)
│ └── octonionic.py # Optional non-associative organization
│
├── domains/
│ └── interferometry/
│ ├── model.py # Two-path interferometer mapping
│ ├── run.py # Baseline vs SDCR vs recovery
│ └── plots.py # Phase and visibility plots
│
├── examples/
│ ├── lindblad_basic.py # Minimal SDCR demonstration
│ ├── null_test.py # Explicit recovery / null test
│ └── visualize_sdcr.py # Hardened, read-only visualization
│
├── scripts/
│ └── run_visualizer.py # Single-entry launcher for visualization
│
├── notebooks/
│ └── sdcr_interferometry_overview.ipynb # Read-only notebook overview
│
├── figures/
│ └── sdcr_core_overview.py # Illustrative overview figure (non-executable)
│
├── tests/
│ ├── test_recovery.py
│ ├── test_symmetry.py
│ ├── test_observables.py
│ └── test_interferometry_domain.py
│
├── README.md
├── LICENSE
└── requirements.txt
core/,domains/,examples/, andtests/contain validated, executable SDCR logicnotebooks/provides read-only, explanatory visual referencesfigures/contains illustrative, presentation-grade overview graphics
(not part of SDCR execution or validation)
This separation preserves scientific cleanliness and avoids conflating illustration with verification.
SDCR-CORE includes visual inspection tools, not interactive dashboards.
- Visualizations are read-only
- All quantum states, operators, time grids, and observables are explicitly validated
- No tunable parameters or sliders are exposed
- Baseline, SDCR-enabled, and recovery evolutions are always shown together
These tools are intended as figure-style companions to the theory, supporting inspection and reproducibility without expanding scope or interpretation.
pip install -r requirements.txtpython examples/lindblad_basic.py
python examples/null_test.pypython -m domains.interferometry.runSingle command from repository root:
python scripts/run_visualizer.pyThis launches the validated, read-only visualization showing:
- coherence decay (baseline vs SDCR vs recovery)
- bounded SDCR phase offset
- explicit recovery limit
A core design principle of sdcr-core is explicit falsifiability.
Every SDCR effect implemented here:
- Depends on exposed control parameters
- Can be switched off to recover standard decoherence
- Produces predictions that vanish in the symmetry-free limit
- Can be tested against null results without ambiguity
The software is designed to make disagreement easy and rigorous, not to enforce a particular interpretation.
This repository represents the first stable software realization of the SDCR framework.
Development proceeds cautiously, with emphasis on:
- correctness
- transparency
- alignment with the published theory
Interfaces and internal structure may evolve incrementally as validated use cases emerge.
This software is released under the MIT License, to encourage open scientific use, independent testing, and reproducibility.
If you use this software in academic work, please cite:
Krüger, M., & Feeney, D. (2025).
Symmetry-Driven Coherence Restoration: Geometric Phase Control, Open-System Dynamics, and Phenomenological Signatures.
Zenodo. https://doi.org/10.5281/zenodo.17942413