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A PyTorch implementation of a Neural Quantum State (NQS) simulator for quantum many-body systems, featuring symmetry-preserving neural networks and advanced sampling techniques.
This project implements a state-of-the-art quantum many-body simulator using Neural Quantum States (NQS). It combines deep learning techniques with quantum physics to simulate quantum systems efficiently. The implementation includes:
- Symmetry-preserving neural network architecture
- Parallel tempering MCMC sampling
- Stochastic Reconfiguration optimization
- Advanced numerical stability features
- Comprehensive physical observables calculation
- SymmetricNQSWaveFunction: Neural network that preserves quantum mechanical symmetries
- MCMCSampler: Advanced Markov Chain Monte Carlo sampling with parallel tempering
- StochasticReconfiguration: Stable optimization method for quantum systems
- Physical Observables:
- Energy and variance
- Magnetization
- Spin-spin correlations
- Structure factor
- Enhanced Visualization: Comprehensive plotting of training metrics and physical quantities
torch>=1.9.0
numpy>=1.19.0
matplotlib>=3.3.0
from quantum_simulator import run_enhanced_simulation
# Run simulation with default parameters
simulator, metrics = run_enhanced_simulation(
n_sites=6,
n_epochs=200,
batch_size=500
)from quantum_simulator import EnhancedQuantumSimulator
# Initialize simulator with custom parameters
simulator = EnhancedQuantumSimulator(
n_sites=8,
learning_rate=0.00002
)
# Configure Stochastic Reconfiguration
simulator.sr = StochasticReconfiguration(
model=simulator.model,
reg_factor=1e-3,
min_svd=1e-6,
batch_size=50
)
# Train and collect metrics
metrics = simulator.train_epoch(batch_size=1000)The simulator achieves stable training and accurate physical results:
- Final Energy: -10.997144
- Final Variance: 0.000086
- Converged magnetization and correlation functions
- Stable learning dynamics throughout training
Example output metrics:
Starting enhanced simulation...
Number of sites: 6
Device: cuda
Epoch 0:
Energy: -10.996608
Variance: 0.000067
Magnetization: -0.082667
Nearest-neighbor correlation: 0.028000
Learning rate: 2.00e-05
Epoch 10:
Energy: -10.996914
Variance: 0.000071
Magnetization: -0.001333
Nearest-neighbor correlation: 0.033600
Learning rate: 2.00e-05
Epoch 20:
Energy: -10.995793
Variance: 0.000134
Magnetization: -0.011333
Nearest-neighbor correlation: 0.027200
Learning rate: 2.00e-05
Epoch 30:
Energy: -10.992054
Variance: 0.000230
Magnetization: 0.050667
Nearest-neighbor correlation: 0.036000
Learning rate: 2.00e-05
Epoch 40:
Energy: -10.993916
Variance: 0.000137
Magnetization: -0.000000
Nearest-neighbor correlation: 0.011200
Learning rate: 2.00e-05
Epoch 50:
Energy: -10.996450
Variance: 0.000088
Magnetization: -0.054667
Nearest-neighbor correlation: 0.012000
Learning rate: 2.00e-05
Epoch 60:
Energy: -10.998333
Variance: 0.000037
Magnetization: -0.023333
Nearest-neighbor correlation: 0.032000
Learning rate: 2.00e-05
Epoch 70:
Energy: -10.999022
Variance: 0.000023
Magnetization: -0.057333
Nearest-neighbor correlation: 0.026400
Learning rate: 2.00e-05
Epoch 80:
Energy: -10.998788
Variance: 0.000032
Magnetization: -0.044000
Nearest-neighbor correlation: 0.028000
Learning rate: 2.00e-05
Epoch 90:
Energy: -10.995109
Variance: 0.000151
Magnetization: -0.146000
Nearest-neighbor correlation: 0.076000
Learning rate: 2.00e-05
Epoch 100:
Energy: -10.995549
Variance: 0.000167
Magnetization: -0.118000
Nearest-neighbor correlation: 0.084800
Learning rate: 1.00e-05
Epoch 110:
Energy: -10.996321
Variance: 0.000093
Magnetization: -0.112667
Nearest-neighbor correlation: 0.049600
Learning rate: 1.00e-05
Epoch 120:
Energy: -10.998017
Variance: 0.000049
Magnetization: -0.092000
Nearest-neighbor correlation: 0.056000
Learning rate: 1.00e-05
Epoch 130:
Energy: -10.997794
Variance: 0.000058
Magnetization: -0.050667
Nearest-neighbor correlation: 0.043200
Learning rate: 1.00e-05
Epoch 140:
Energy: -10.998185
Variance: 0.000065
Magnetization: -0.044667
Nearest-neighbor correlation: 0.088000
Learning rate: 1.00e-05
Epoch 150:
Energy: -10.997000
Variance: 0.000070
Magnetization: -0.046000
Nearest-neighbor correlation: -0.000800
Learning rate: 1.00e-05
Epoch 160:
Energy: -10.997014
Variance: 0.000111
Magnetization: -0.024000
Nearest-neighbor correlation: 0.046400
Learning rate: 1.00e-05
Epoch 170:
Energy: -10.996198
Variance: 0.000121
Magnetization: -0.041333
Nearest-neighbor correlation: 0.002400
Learning rate: 5.00e-06
Epoch 180:
Energy: -10.997696
Variance: 0.000103
Magnetization: -0.030000
Nearest-neighbor correlation: 0.052800
Learning rate: 2.50e-06
Epoch 190:
Energy: -10.996375
Variance: 0.000098
Magnetization: -0.080000
Nearest-neighbor correlation: 0.048000
Learning rate: 2.50e-06
Simulation completed!
Final energy: -10.997144
Final variance: 0.000086
The project uses a modular architecture with the following key components:
Detailed documentation for each component:
- Implements symmetry-preserving neural network
- Uses residual connections and layer normalization
- Separates real and imaginary components
- Implements parallel tempering
- Handles multiple Markov chains
- Includes proper metropolis updates
- Implements stable SR optimization
- Uses SVD with regularization
- Includes batched computation
If you use this code in your research, please cite:
@software{nqs-quantum-simulator,
author = {RaheesAhmed},
title = {Neural Quantum State Simulator},
year = {2024},
publisher = {GitHub},
url = {https://github.com/raheesahmed/nqs-quantum-simulator}
}- Thanks to the PyTorch team for their excellent deep learning framework
- Special thanks to the quantum physics community for theoretical foundations
- RaheesAhmed - [email protected]
- Project Link: https://github.com/raheesahmed/nqs-quantum-simulator