This circuit discriminates between the states |0⟩ and |ψ₂⟩ unambiguously, using an ancilla qubit.
```python
from qiskit import QuantumCircuit
import math
# Create a circuit with 2 qubits and 2 classical bits
qc = QuantumCircuit(2, 2)
# Prepare the state |ψ₂⟩ = cos(θ)|0⟩ + sin(θ)|1⟩ on qubit 0
theta = math.radians(30) # θ = 30 degrees
qc.ry(2 * theta, 0)
# Implement unambiguous state discrimination between |0⟩ and |ψ₂⟩
qc.cx(0, 1)
qc.ry(-2 * theta, 1)
# Measure the ancilla qubit to determine the state
qc.measure(1, 0)
# Measure the system qubit
qc.measure(0, 1)
```'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"}]}\''