Description

This quantum circuit creates a 4-qubit Dicke state with 2 excitations and subsequently measures all qubits.

Qiskit Circuit Code

```python
from qiskit import QuantumCircuit
import numpy as np

# Create a circuit with 4 qubits and 4 classical bits
qc = QuantumCircuit(4, 4)

# Define the amplitudes for the 4-qubit Dicke state with 2 excitations
state_vector = np.zeros(16, dtype=complex)

# Indices of the basis states with exactly two qubits in state '1'
indices = [
    int('0011', 2),  # |0011⟩
    int('0101', 2),  # |0101⟩
    int('0110', 2),  # |0110⟩
    int('1001', 2),  # |1001⟩
    int('1010', 2),  # |1010⟩
    int('1100', 2)   # |1100⟩
]

# Set the amplitudes for these states to 1/√6
amplitude = 1 / np.sqrt(6)
for idx in indices:
    state_vector[idx] = amplitude

# Initialize the qubits to the defined Dicke state
qc.initialize(state_vector, [0, 1, 2, 3])

# Measure all qubits
qc.measure([0, 1, 2, 3], [0, 1, 2, 3])
```

Quantum Execution Results

{
  "backend": "ibm_sherbrooke",
  "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"
}

Download Results