This repository contains a comprehensive framework for simulating quantum circuits under depolarizing noise and applying fidelity optimization techniques for fidelity correction and optimization.
- Quantum Circuit Simulation using Cirq
- Depolarizing Noise Modelling for NISQ-era quantum devices
- Error Mitigation Techniques: Deterministic, Stochastic, Bayesian Optimization
- Machine Learning-based Fidelity Enhancement using TensorFlow
- Reinforcement Learning (PPO-based) for Adaptive Optimization
- Variational Models for parameterized quantum error correction
https://colab.research.google.com/drive/1oE71SeZeaZ03FLcmhx7kDK2NWJeAVBC3
pip install cirq tqdm tensorflow bayesian-optimization stable-baselines3 shimmy gym- Execute the quantum circuit simulation.
- Apply ML-based fidelity correction techniques.
- Compare performance across noise levels.
- Randomized Rx circuits initialized with Hadamard gates.
- CNOT entanglement layers for generating correlations.
- Depolarizing noise channel applied at each layer.
We define a statistical fidelity metric:
[ F = e^{-\eta} \frac{(p + C)}{2} ]
where:
- p = Probability of measuring ‘1’ outcomes
- C = Mean absolute correlation between adjacent qubits
- e^{-\eta} = Exponential noise decay factor
This metric is computationally efficient and strongly correlates with conventional fidelity measures like Uhlmann fidelity and Trace Distance.
| Method | Description |
|---|---|
| Deterministic Correction | Simple heuristic-based correction for low-noise conditions. |
| Stochastic Sampling | Monte Carlo-based fidelity estimation using small perturbations. |
| Bayesian Optimization | Gaussian Process-based search for optimal correction parameters. |
| Gradient-Based Optimization (TF) | TensorFlow-powered dynamic correction with backpropagation. |
| Reinforcement Learning (PPO) | RL agent learns optimal fidelity-enhancing actions. |
| Variational Model (Single Parameter) | Trigonometric correction model optimizing a single parameter θ. |
| Neural Variational Model | Neural network learns fidelity correction for arbitrary configurations. |
- Baseline Fidelity (No Correction): ~0.25 in noiseless conditions.
- Best Achieved Fidelity: 0.45+ using Reinforcement Learning & Variational Models.
- Performance Hierarchy: RL > Variational > Bayesian > Gradient-based > Stochastic > Deterministic.
- Higher Noise → Diminishing returns for all methods.
-
Qubits initialized to |0⟩ and evolved through Rx rotations + CNOT layers.
-
Depolarizing Noise Model:
[ E(\rho) = (1-\eta)\rho + \eta \frac{I}{2} ]
-
Measurements performed across 100 shots per circuit.
-
Input Features: Probability of ‘1’ outcomes, mean qubit correlation, noise level.
-
Output: Corrected fidelity after optimization.
-
Optimization Criteria:
[ \text{Optimize } (p + C) / 2 \text{ under constraints} ]
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State Space: (p, C, noise level)
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Action Space: (Δp, ΔC) small corrections applied to improve fidelity.
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Reward Function:
[ R = e^{-\eta} \frac{(p + \delta p) + (C + \delta C)}{2} ]
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Training Strategy: PPO with advantage function estimation.
- Single-Parameter Model: Uses sinusoidal variations for smooth corrections.
- Neural Network Model: Learns global corrections over circuit configurations.
- Extending to larger grids & real hardware validation.
- Integrating phase-sensitive corrections for coherent noise models.
- Testing advanced RL policies (SAC, TRPO) & quantum-aware optimizations.
If you use this repository in your research, please cite:
Apostolos Panagiotopoulos, Quantum Circuit Classical Simulation and Fidelity Benchmarking, 2025.
Full Report: cirqQuantumCircuitFidelityBenchmark.pdf
quantum-computingcirqtensorflowbayesian-optimizationreinforcement-learning
Apostolos Panagiotopoulos
[email protected]
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MIT License
Copyright (c) 2025 Apostolos Panagiotopoulos
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