# W state (Qiskit)
[[w-state|W state]] implementation using Qiskit. The three-qubit W state $\lvert W\rangle = (\lvert 001\rangle + \lvert 010\rangle + \lvert 100\rangle)/\sqrt{3}$ is prepared using the recursive decomposition $\lvert W_3\rangle = \frac{1}{\sqrt{3}}\lvert 1\rangle\lvert 00\rangle + \sqrt{\frac{2}{3}}\lvert 0\rangle\lvert W_2\rangle$.

```python
import numpy as np
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector

qc = QuantumCircuit(3)

# Step 1: Ry on q[0] to set amplitude 1/sqrt(3) for |1> (the |100> term)
theta = 2 * np.arccos(np.sqrt(2/3))
qc.ry(theta, 0)  # sqrt(2/3)|0> + 1/sqrt(3)|1>

# Step 2: anti-controlled preparation of |W_2> = (|01> + |10>)/sqrt(2) on q[1],q[2]
# "anti-controlled" = apply when q[0]=0, achieved by flipping q[0] around the block
qc.x(0)
qc.cx(0, 2)    # X on q[2] (sets the first excitation)
qc.ch(0, 1)    # H on q[1] (creates superposition)
qc.ccx(0, 1, 2) # Toffoli: restores q[2] when q[1] also fired
qc.x(0)

print(Statevector(qc))
# Statevector([0, 0.57735027, 0.57735027, 0, 0.57735027, 0, 0, 0], dims=(2,2,2))
# non-zero at |001>, |010>, |100> with amplitude 1/sqrt(3)
```