This quantum circuit creates a superposition state, encodes it, simulates a bit-flip error, applies an error correction, decodes the state, and measures the corrected qubit.
```python
from qiskit import QuantumCircuit
# Create circuit with 5 qubits and 1 classical bit
qc = QuantumCircuit(5, 1)
# Prepare the initial state on qubit 0 (e.g., superposition state)
qc.h(0)
# Encoding: Spread the state of qubit 0 to qubits 1 and 2 (bit-flip code)
qc.cx(0, 1)
qc.cx(0, 2)
# Introduce a bit-flip error on qubit 1 (simulate error)
qc.x(1)
# Error Correction using two ancilla qubits (qubits 3 and 4)
# Syndrome extraction
qc.cx(0, 3)
qc.cx(1, 3)
qc.cx(0, 4)
qc.cx(2, 4)
# Error detection and correction
qc.ccx(3, 4, 1) # Correct qubit 1 based on the syndrome
# Decoding: Retrieve the original state from qubits 0, 1, 2
qc.cx(0, 2)
qc.cx(0, 1)
# Measure the corrected qubit
qc.measure(0, 0)
```'Failed to run program: \'409 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"}]}\''