I am trying to implement a code correction error in jupyter notebook using Pennylane. I create the superposition alpha|000> + beta|111>

I rotate the state to apply a weak error

I measure Z1@Z2 and Z1@Z3 to check for errors and fix them using an X gate.

Then I try to plot the results but it appears like nothing is being fixed why is that?

```
# Importing necessary libraries
import pennylane as qml
import numpy as np
import matplotlib.pyplot as plt
import random
def plot_probs(probs, description=""):
states = [f"|{i:03b}⟩" for i in range(8)]
plt.bar(states, probs)
plt.xlabel('States')
plt.ylabel('Probability')
plt.title(f'Probability distribution after {description}')
plt.show()
# Print the probabilities
print(f"Probabilities of states after {description}:")
for i, p in enumerate(probs):
print(f"State |{i:03b}⟩: {p:.4f}")
print("\n")
# Define the number of qubits
n_qubits = 3
# Initialize a device
dev = qml.device('default.qubit', wires=n_qubits, shots=1000)
# Define the initial state preparation function
def initial_state(alpha, beta):
qml.RY(2 * np.arccos(alpha), wires=0)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[0, 2])
# Define the weak error operation
def apply_weak_error():
qubit_to_flip = random.randint(0, 2)
epsilon = np.pi / 10
qml.RX(epsilon, wires=qubit_to_flip)
@qml.qnode(dev)
def circuit1(alpha, beta):
initial_state(alpha, beta)
apply_weak_error()
return qml.probs(wires=[0, 1, 2])
# Define the circuit with error correction
@qml.qnode(dev)
def circuit2(alpha, beta):
initial_state(alpha, beta)
apply_weak_error()
# Measure the stabilizers
Z1Z2 = qml.sample(qml.PauliZ(0) @ qml.PauliZ(1))
Z1Z3 = qml.sample(qml.PauliZ(0) @ qml.PauliZ(2))
# Define error correction based on the stabilizer measurements
if Z1Z2 == 1 and Z1Z3 == 1:
pass
elif Z1Z2 == -1 and Z1Z3 == -1:
qml.PauliX(wires=0)
elif Z1Z2 == -1 and Z1Z3 == 1:
qml.PauliX(wires=1)
elif Z1Z3 == 1 and Z1Z2 == -1:
qml.PauliX(wires=2)
# Measure the corrected state after error correction
corrected_state = qml.probs(wires=[0, 1, 2])
# Return stabilizer measurements and corrected state
return Z1Z2, Z1Z3, corrected_state
# Parameters for the state |ψ⟩ = α|000⟩ + β|111⟩
alpha = 0.4
beta = np.sqrt(1 - alpha ** 2)
probs_error = circuit1(alpha, beta)
plot_probs(probs_error, description="weak error")
# Run the circuit with error correction
Z1Z2, Z1Z3, corrected_state = circuit2(alpha, beta)
plot_probs(corrected_state, "Corrected State After Error Correction")
```