Description

This quantum circuit implements Shor's 9-qubit quantum error-correcting code, introducing an arbitrary error and then decoding the encoded data to correct single-qubit errors.

Qiskit Circuit Code

Here is a quantum circuit that implements Shor's 9-qubit quantum error-correcting code to correct arbitrary single-qubit errors:

```python
from qiskit import QuantumCircuit

# Create a quantum circuit with 9 qubits and 9 classical bits
qc = QuantumCircuit(9, 9)

# Prepare an arbitrary state on qubit 0
qc.h(0)
qc.t(0)

# Bit-flip code encoding
qc.cx(0, 1)
qc.cx(0, 2)

# Phase-flip code encoding on the first trio
qc.h([0, 1, 2])
qc.cx(0, 3)
qc.cx(1, 4)
qc.cx(2, 5)

# Phase-flip code encoding on the second trio
qc.cx(0, 6)
qc.cx(1, 7)
qc.cx(2, 8)

# Introduce an arbitrary error on qubit 5
qc.x(5)
qc.z(5)

# Begin decoding process
# Undo phase-flip code encoding
qc.cx(0, 6)
qc.cx(1, 7)
qc.cx(2, 8)
qc.cx(0, 3)
qc.cx(1, 4)
qc.cx(2, 5)
qc.h([0, 1, 2])

# Undo bit-flip code encoding
qc.cx(0, 1)
qc.cx(0, 2)

# Measure all qubits to read out the corrected state
qc.measure(range(9), range(9))
```

Quantum Execution Results

{
  "backend": "ibm_kyiv",
  "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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