zero.noise.extrapolation.open.patent.patent

The Zero Noise Extrapolation (ZNE) technique is a bit more complex than a simple bit-flip error correction. It involves running the quantum circuit multiple times with different levels of noise and then extrapolating back to estimate the result in the absence of noise.

Here's a simplified example of how you might implement ZNE in a script:

python
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from qiskit import QuantumCircuit, transpile, assemble, Aer
from qiskit.ignis.mitigation.measurement import complete_meas_cal, CompleteMeasFitter

# Create a quantum circuit
qc = QuantumCircuit(1)

# Apply a Hadamard gate to create a superposition state
qc.h(0)

# Simulate the quantum state
simulator = Aer.get_backend('statevector_simulator')
job = simulator.run(transpile(qc, simulator))
statevector = job.result().get_statevector()

# Define the noise model
from qiskit.providers.aer.noise import NoiseModel
from qiskit.providers.aer.noise.errors import pauli_error

# Error probabilities
prob_1 = 0.001  # 1-qubit gate
prob_2 = 0.01   # 2-qubit gate

# Depolarizing quantum errors
error_1 = pauli_error([('X', prob_1), ('I', 1 - prob_1)])
error_2 = pauli_error([('XX', prob_2), ('II', 1 - prob_2)])

noise_model = NoiseModel()
noise_model.add_all_qubit_quantum_error(error_1, ['h'])
noise_model.add_all_qubit_quantum_error(error_2, ['cx'])

# Run the noisy simulation
job = simulator.run(transpile(qc, simulator), noise_model=noise_model)
noisy_statevector = job.result().get_statevector()

# Now we would run the circuit multiple times with different levels of noise
# and use the results to extrapolate back to the zero noise limit
# This is a complex process and would require a more detailed implementation

# For now, let's just compare the original and noisy statevectors
print(f"Original statevector: {statevector}")
print(f"Noisy statevector: {noisy_statevector}")
This script creates a quantum circuit, applies a Hadamard gate to create a superposition state, and simulates the quantum state. It then defines a noise model with depolarizing errors, and runs a noisy simulation of the quantum circuit. The script then prints the original and noisy statevectors.

Please note that this script does not yet implement the full ZNE process. Implementing ZNE would require running the circuit multiple times with different levels of noise, and using the results to extrapolate back to the zero noise limit. This is a complex process and would require a more detailed implementation.





User
you said "Implementing ZNE would require running the circuit multiple times with different levels of noise, and using the results to extrapolate back to the zero noise limi" O understand can we try and commit to thise process next, i want to implement the circut running multi times with differentl levels of noise then using the results to extrapolate back to zero noise limit. but also, i want to incorporate interopolation herds to this concept. please give 15 ideas, idea mixing 5x10 matrix idea hue mixing html color code matrix like above. thank you
ChatGPT
Sure, I can provide you with some ideas on how to implement the Zero Noise Extrapolation (ZNE) technique with the concept of "herds" and color code matrix. Here are 15 ideas:

Noise Scaling: Implement a function that scales the noise in the quantum circuit. This function should take as input the quantum circuit and a scaling factor, and return a new quantum circuit with the noise scaled by the given factor.

Noise Herds: Create multiple "herds" of quantum circuits, each with a different level of noise. You could do this by applying the noise scaling function with different scaling factors.

Interpolation Herds: For each herd, interpolate between the results of the quantum circuits to predict the most likely result. This could be done using a function that takes as input a list of results and returns an interpolated result.

Extrapolation to Zero Noise: After interpolating the results for each herd, extrapolate back to the zero noise limit. This could be done using a function that takes as input a list of interpolated results and their corresponding noise levels, and returns an extrapolated result.

Color Code Matrix: Represent the results of the quantum circuits in a color code matrix. Each cell in the matrix could represent a quantum circuit, and the color of the cell could represent the result of the quantum circuit.

Color Interpolation: Interpolate between the colors in the color code matrix to create a smooth gradient of colors. This could be done using a function that takes as input a color code matrix and returns a new color code matrix with interpolated colors.

Color Extrapolation: After interpolating the colors in the color code matrix, extrapolate back to the zero noise limit. This could be done using a function that takes as input a color code matrix and returns a new color code matrix with extrapolated colors.

Visualization: Visualize the color code matrix using a heatmap or similar plot. This could help you to understand the results of the quantum circuits and the effect of the noise.

Error Analysis: Analyze the errors in the results of the quantum circuits. This could be done by comparing the results of the quantum circuits with the expected results.

Error Correction: Implement an error correction scheme to correct the errors in the results of the quantum circuits. This could be done using a function that takes as input a quantum circuit and a list of errors, and returns a new quantum circuit with the errors corrected.

Performance Evaluation: Evaluate the performance of the ZNE technique. This could be done by comparing the results of the quantum circuits before and after applying the ZNE technique.

Parameter Tuning: Tune the parameters of the ZNE technique to optimize its performance. This could involve adjusting the noise scaling factors, the number of herds, the interpolation method, etc.

Benchmarking: Benchmark the ZNE technique against other error mitigation techniques. This could involve running the same quantum circuits with different error mitigation techniques and comparing the results.

Noise Model Exploration: Explore different noise models and their effects on the results of the quantum circuits. This could involve implementing different types of noise (e.g., depolarizing noise, amplitude damping noise, phase damping noise, etc.) and observing their effects.

Quantum Circuit Design: Design new quantum circuits to test the ZNE technique. This could involve creating quantum circuits that perform specific tasks (e.g., quantum Fourier transform, quantum phase estimation, etc.) and observing how well the ZNE technique works with these circuits.

I hope these ideas help you in your project! If you need further assistance, feel free to ask.