A Python package for simulating and analyzing quantum error correction thresholds, with focus on the Surface Code.
This package provides tools to:
- Simulate the rotated Surface Code with configurable distance
- Apply various noise models (depolarizing, biased, correlated)
- Decode errors using the MWPM algorithm
- Estimate error correction thresholds via Monte Carlo simulation
- Perform finite-size scaling analysis
- Generate publication-quality visualizations
The threshold theorem states that if the physical error rate is below a critical threshold, quantum error correction can suppress logical errors to arbitrarily low levels by increasing the code distance.
For the surface code with depolarizing noise:
- Threshold: ~1% (Fowler et al., 2012)
- Below threshold: logical error rate scales as exp(-αd)
- Above threshold: error correction fails
Simulation Results (Distance 3-11, 1000 trials):
-
Estimated Threshold:
$p_{th} \approx 1.00%$ -
Confidence Interval:
$0.99% - 1.01%$ - Computation Time: ~4.5s
Error rates for different code distances. The crossing point indicates the threshold.
Visualization of the d=11 lattice with Qubit/Stabilizer layout.
Logical error rate suppression below threshold (exponential decay).
Universal scaling behavior near the phase transition.
# Clone the repository
git clone https://github.com/rasidi3112/qec-threshold-simulator.git
cd qec-threshold-simulator
# Install dependencies
pip install -r requirements.txtfrom qec_threshold import SurfaceCode, ThresholdEstimator
# Create surface code
code = SurfaceCode(distance=5)
# Run threshold estimation
estimator = ThresholdEstimator(
distances=[3, 5, 7],
num_trials=1000
)
result = estimator.run_threshold_estimation()
print(f"Threshold: {result.estimated_threshold:.4f}")# Run simulation with default parameters
python run_simulation.py
# Specify parameters
python run_simulation.py --distances 3 5 7 9 --trials 1000 --output results/from qec_threshold import (
SurfaceCode,
MWPMDecoder,
DepolarizingChannel,
ThresholdEstimator,
ThresholdVisualizer,
)
# Create and simulate
code = SurfaceCode(distance=5)
channel = DepolarizingChannel(error_probability=0.01)
decoder = MWPMDecoder(code)
# Apply errors and decode
import numpy as np
rng = np.random.default_rng(42)
errors = channel.apply(code.num_data_qubits, rng)
x_syndrome, z_syndrome = code.measure_syndrome(errors)
x_correction, z_correction = decoder.decode(x_syndrome, z_syndrome)qec_threshold/
├── __init__.py # Package exports
├── core/ # Core components
│ ├── pauli.py # Pauli operators
│ └── surface_code.py # Surface code implementation
├── decoders/ # Decoder algorithms
│ └── mwpm.py # MWPM decoder
├── noise_models/ # Noise channels
│ ├── depolarizing.py # Depolarizing channel
│ ├── biased.py # Biased noise
│ └── correlated.py # Correlated noise
├── analysis/ # Analysis tools
│ ├── threshold_estimator.py
│ └── finite_size_scaling.py
└── visualization/ # Plotting utilities
├── threshold_plots.py
└── advanced_plots.py
-
Fowler, A. G., et al. "Surface codes: Towards practical large-scale quantum computation." Physical Review A 86.3 (2012): 032324. arXiv:1208.0928
-
Dennis, E., et al. "Topological quantum memory." Journal of Mathematical Physics 43.9 (2002): 4452-4505.
-
Kitaev, A. Y. "Fault-tolerant quantum computation by anyons." Annals of Physics 303.1 (2003): 2-30.
This is an educational implementation demonstrating QEC threshold concepts. For research-grade simulations, consider using established libraries like Stim or PyMatching.
This is an open source project released under the MIT License.
You are free to use, modify, and distribute this software. See LICENSE file for details.