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Topological Quantum Compiler

PyPI version CI Documentation Code style: black License: MIT

The first universal compiler for quantum computers based on topological principles.

TQC revolutionizes quantum computing by moving beyond fragile gate-based operations to fault-tolerant anyonic braiding. By encoding quantum information in the topological properties of anyonic quasiparticles, TQC provides inherent protection against environmental decoherence and computational errors.

🚀 Key Innovations

  • Topological Protection: Inherently fault-tolerant quantum computation through anyonic braiding
  • Universal Compilation: Translate any quantum circuit into braided operations
  • Advanced Optimization: Solovay-Kitaev-style algorithms adapted for braid optimization
  • Multiple Anyon Types: Support for Fibonacci, Ising, and other anyonic systems
  • Efficient Simulation: Tensor network simulation of many-anyon systems
  • Rich Visualization: Generate beautiful braid diagrams and topological visualizations

🌟 Why TQC Matters

Traditional quantum computers suffer from fundamental limitations:

  • Fragile qubits that lose coherence rapidly
  • High error rates requiring extensive quantum error correction
  • Environmental sensitivity limiting practical applications
  • Scalability challenges due to noise accumulation

TQC solves these problems through topological quantum computation:

  • Natural fault tolerance - protected by energy gaps
  • Stable against local perturbations - only global changes affect computation
  • Polynomial scaling - complexity grows manageable with system size
  • Intrinsic error suppression - topological protection built-in

🔬 Quick Example

from tqc import TopologicalCompiler, FibonacciAnyons
from qiskit import QuantumCircuit

# Create a Bell state circuit
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
qc.measure_all()

# Compile to topological braids
compiler = TopologicalCompiler(anyon_type=FibonacciAnyons())
result = compiler.compile(qc)

print(f"Compiled to {len(result.braid_program)} braids")
print(f"Estimated fidelity: {result.fidelity_estimate:.4f}")

# Simulate the braided computation
sim_result = result.braid_program.simulate(shots=1000)
print(f"Results: {sim_result.counts}")

# Generate visualization
result.braid_program.visualize_braid("bell_state.svg")

🧮 Scientific Foundation

TQC is built on decades of theoretical advances in:

  • Topological Quantum Field Theory - Mathematical framework for anyonic systems
  • Modular Tensor Categories - Algebraic structure of anyonic braiding
  • Solovay-Kitaev Algorithm - Efficient approximation of quantum gates
  • Tensor Network Theory - Efficient classical simulation methods

📈 Performance Benefits

Traditional Gates Topological Braids
Exponential error accumulation Polynomial error suppression
Requires active error correction Natural fault tolerance
Sensitive to all noise sources Protected by energy gaps
Limited coherence times Stable operation

🎯 Applications

TQC enables breakthrough applications in:

  • Quantum Chemistry - Fault-tolerant molecular simulation
  • Cryptography - Robust quantum key distribution
  • Machine Learning - Stable quantum neural networks
  • Optimization - Reliable quantum annealing
  • Simulation - Large-scale many-body physics

🏗️ Architecture

graph TD
    A[Quantum Circuit] --> B[Topological Compiler]
    B --> C[Anyonic Mapping]
    B --> D[Braid Generation]
    B --> E[Optimization Engine]

    C --> F[Fusion Tree Basis]
    D --> G[Braid Word]
    E --> H[Simplified Braids]

    F --> I[Anyonic Simulator]
    G --> I
    H --> I

    I --> J[Measurement Results]
    I --> K[Braid Visualization]

🤝 Community

Join the topological quantum computing revolution:

📄 Citation

If you use TQC in your research, please cite:

@software{topological_quantum_compiler,
  title = {Topological Quantum Compiler: Universal Compilation via Anyonic Braiding},
  author = {TQC Team},
  year = {2025},
  url = {https://github.com/tqc/topological-quantum-compiler},
  version = {0.1.0}
}

"The future of quantum computing is topological." - TQC Team