# Optimizing state overlap / multi-qubit qml.expval.Hermitian()

**URL:** <https://discuss.pennylane.ai/t/optimizing-state-overlap-multi-qubit-qml-expval-hermitian/84>\
**Category:** PennyLane Help\
**Created:** [February 14, 2019, 12:44am UTC](https://discuss.pennylane.ai/t/optimizing-state-overlap-multi-qubit-qml-expval-hermitian/84 "2019-02-14T00:44:05Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![josh](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/josh/32/100_2.png) [@josh](https://discuss.pennylane.ai/u/josh)\
**Post date:** [February 14, 2019, 4:47am UTC](https://discuss.pennylane.ai/t/optimizing-state-overlap-multi-qubit-qml-expval-hermitian/84/3 "2019-02-14T04:47:10Z")

</div>

And just for completeness, here is the full optimization:

```python
import pennylane as qml
from pennylane import numpy as np

dev = qml.device('default.qubit', wires=2)

@qml.qnode(dev)
def circuit(x, target_observable=None):
    qml.RX(x[0], wires=0)
    qml.RY(x[1], wires=0)
    qml.RZ(x[2], wires=0)
    qml.CNOT(wires=[0, 1])
    return qml.expval.Hermitian(target_observable, wires=[0, 1])

target_state = 1/np.sqrt(2) * np.array([1,0,0,1])
target_herm_op = np.outer(target_state.conj(), target_state)

weights = np.array([0.5, 0.1, 0.2])

def cost(weights):
    return np.abs(circuit(weights, target_observable=target_herm_op)-1)**2

opt = qml.AdamOptimizer(stepsize=0.4)

for i in range(2000):
    weights = opt.step(cost, weights)

    if (i+1) % 20 == 0:
        print('Cost after step {:5d}: {: .7f}'.format(i+1, cost(weights)))

fidelity = circuit(weights, target_observable=target_herm_op)

print('Optimized rotation angles: {}'.format(weights))
print('Final fidelity: {}'.format(fidelity))

# this is a hidden/undocumented attribute of the default.qubit
# plugin, that is not part of the API.
print('Output state: {}'.format(dev._state))

```

which produces the output

```python
Optimized rotation angles: [1.44393011 1.57000406 1.44393011]
Final fidelity: 0.9999999974878844
Output state: [0.70714217-0.00027786j, 0.00000000+0.j 0.00000000+0.j 0.70707128-0.00027786j]

```

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