Noise Models and Simulations in Quantum Computing

Table of Contents

1. Introduction
2. Why Simulate Noise?
3. Types of Quantum Noise
4. Basics of Noise Modeling
5. Qiskit’s Noise Model Framework
6. Creating Custom Noise Models
7. Bit-Flip and Phase-Flip Errors
8. Depolarizing Noise
9. Amplitude Damping
10. Phase Damping
11. Using Qiskit’s NoiseModel Class
12. Applying Noise in Circuit Execution
13. Noise-Aware Simulation Backend
14. Realistic Noise from Real Devices
15. Visualizing the Effect of Noise
16. Error Mitigation Basics
17. Noise vs Decoherence
18. Quantum Error Correction and Noise
19. Best Practices for Simulating Noise
20. Conclusion

1. Introduction

Quantum systems are inherently noisy due to decoherence, gate errors, and readout inaccuracies. Simulating noise helps developers understand how algorithms behave under realistic conditions.

2. Why Simulate Noise?

• Evaluate algorithm robustness
• Estimate success probability
• Develop error mitigation techniques
• Benchmark against real hardware

3. Types of Quantum Noise

• Gate errors (imprecise unitaries)
• Decoherence (T1, T2 processes)
• Crosstalk
• Readout error

4. Basics of Noise Modeling

Noise is represented using quantum channels:

• Kraus operators
• Lindblad master equations
• Pauli noise

5. Qiskit’s Noise Model Framework

Qiskit Aer allows defining and simulating various noise types using:

from qiskit.providers.aer.noise import NoiseModel

6. Creating Custom Noise Models

from qiskit.providers.aer.noise.errors import pauli_error
error = pauli_error([('X', 0.1), ('I', 0.9)])

7. Bit-Flip and Phase-Flip Errors

bit_flip = pauli_error([('X', p), ('I', 1 - p)])
phase_flip = pauli_error([('Z', p), ('I', 1 - p)])

8. Depolarizing Noise

from qiskit.providers.aer.noise.errors import depolarizing_error
error = depolarizing_error(0.05, 1)  # 5% error on 1-qubit gate

9. Amplitude Damping

from qiskit.providers.aer.noise.errors import amplitude_damping_error
error = amplitude_damping_error(gamma=0.1)

10. Phase Damping

from qiskit.providers.aer.noise.errors import phase_damping_error
error = phase_damping_error(gamma=0.1)

11. Using Qiskit’s NoiseModel Class

noise_model = NoiseModel()
noise_model.add_all_qubit_quantum_error(error, ['u3', 'cx'])

12. Applying Noise in Circuit Execution

from qiskit import Aer, execute
backend = Aer.get_backend('qasm_simulator')
result = execute(qc, backend, noise_model=noise_model).result()

13. Noise-Aware Simulation Backend

qasm_simulator supports all noise models:

simulate = Aer.get_backend('qasm_simulator')

14. Realistic Noise from Real Devices

from qiskit_ibm_provider import IBMProvider
backend = IBMProvider().get_backend('ibmq_belem')
noise_model = NoiseModel.from_backend(backend)

15. Visualizing the Effect of Noise

Compare ideal and noisy histograms:

from qiskit.visualization import plot_histogram
plot_histogram([ideal_counts, noisy_counts], legend=['Ideal', 'Noisy'])

16. Error Mitigation Basics

Simulations with noise also enable study of:

• Readout error mitigation
• Zero-noise extrapolation
• Probabilistic error cancellation

17. Noise vs Decoherence

• Noise: Random gate-level error
• Decoherence: Environment-induced state loss (T1, T2)

18. Quantum Error Correction and Noise

Simulation is used to test:

• Code performance (e.g., Shor, Surface)
• Threshold behavior
• Syndrome measurement fidelity

19. Best Practices for Simulating Noise

• Start with simple models (bit-flip)
• Add realistic noise from device backends
• Always benchmark against ideal execution
• Simulate with sufficient shots (≥1000)

20. Conclusion

Noise simulation is essential for understanding real-world performance of quantum circuits. Qiskit provides a robust toolkit for modeling, injecting, and analyzing noise, empowering developers to design more resilient quantum algorithms.