Description

This quantum circuit simulates a phase-flip error on a qubit and corrects it using a phase-flip error correction code.

Qiskit Circuit Code

```python
from qiskit import *

# Create a quantum circuit with 3 qubits and 3 classical bits
qc = QuantumCircuit(3, 3)

# Encode the qubit using a phase-flip error correction code
# Step 1: Apply Hadamard to the data qubit to change basis
qc.h(0)

# Step 2: Encode the qubit using CNOT gates (preparing for phase-flip error correction)
qc.cx(0, 1)
qc.cx(0, 2)

# Introduce a phase-flip error on qubit 1 (simulate error)
qc.z(1)

# Decode the qubits to correct the error
qc.cx(0, 1)
qc.cx(0, 2)

# Step 3: Apply Hadamard to return to the computational basis
qc.h(0)

# Measure all qubits
qc.measure([0, 1, 2], [0, 1, 2])
```

Quantum Execution Results

{
  "backend": "ibm_brisbane",
  "error": "\u0027Failed to run program: \\\u0027409 Client Error: Conflict for url: https://api.quantum.ibm.com/runtime/jobs. {\"errors\":[{\"message\":\"You have reached the limit of 3 pending  jobs. Please wait for a job to complete or cancel one before submitting anything new.\",\"code\":3458,\"solution\":\"Wait until some previous jobs were finished. You can cancel pending jobs to run new jobs.\",\"more_info\":\"https://docs.quantum-computing.ibm.com/errors\"}]}\\\u0027\u0027",
  "status": "failed"
}

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