# Optimize with qml.state() and autograd

**URL:** <https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920>\
**Category:** PennyLane Help\
**Created:** [March 16, 2021, 9:36am UTC](https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920 "2021-03-16T09:36:24Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Zedd](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/zedd/32/2164_2.png) [@Zedd](https://discuss.pennylane.ai/u/Zedd)\
**Post date:** [March 16, 2021, 9:36am UTC](https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920/1 "2021-03-16T09:36:24Z")

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Hello, I’m trying to calculate inner products of quantum states directly from `qml.state()` and build kernel matrix. My optimizer is `qml.AdamOptimizer()`.

And I got `TypeError: must be real number, not ArrayBox` when assign quantum state vectors to an numpy array element wise. It seems like the returned state is `ArrayBox` type and cannot be assigned to a numpy array element.

Is there any way to solve this?😀  
I also tried to use `ArrayBox._value` to assign. However in this way the weights just stayed the same and didn’t update.

Below are my codes:

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

n_qubits = 5
n_layers = 2
dev = qml.device("default.qubit", wires=n_qubits)

from pennylane.templates import QAOAEmbedding
@qml.qnode(dev, diff_method='backprop')
def circuit(weights, feature):
    QAOAEmbedding(features=feature, weights=weights, wires=range(n_qubits))
    return qml.state()

from pennylane.init import qaoa_embedding_uniform
weights = qaoa_embedding_uniform(n_layers,n_qubits)
#print(weights)

N = 10
d = 4
X = np.random.uniform(size=(N,d))
#print(X)

# map x to quantum state |x>
def encoder(weights, X):
    M = X.shape[0]
    features = np.empty((M,2**n_qubits),dtype='complex_')
    for i in range(M):
        # failed here
        features[i] = circuit(weights,X[i])
        # features[i] = circuit(weights,X[i])._value
    return features
# kernel matrix
def matrix(features):
    # <x_i|x_j>
    t1 = features @ features.conj().T
    # |<x_i|x_j>|^2
    t2 = np.multiply(t1,t1.conj())
    return np.absolute(t2)

def cost_naive(weights,X=None):
    features = encoder(weights,X)
    K = matrix(features)
    return K.sum()

optim = qml.AdamOptimizer()
for i in range(10):
    weights, loss = optim.step_and_cost(cost_naive,weights,X=X)
    print(weights[0])
    print(loss)

```

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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:** [March 16, 2021, 11:09am UTC](https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920/2 "2021-03-16T11:09:45Z")

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Hi @Zedd!

The issue here is that Autograd does not support index assignment; in particular the line

```python
features[i] = circuit(weights,X[i])

```

where the output of `circuit` is being assigned to the `i`th element of `features`.

This is a common ‘gotcha’ of Autograd; the [Autograd tutorial](https://github.com/HIPS/autograd/blob/master/docs/tutorial.md#supported-and-unsupported-parts-of-numpyscipy) lists other parts of NumPy/SciPy that are not supported by Autograd.

But that’s all good! Rather than using array index assignment, we can rewrite this to use lists instead:

```python
features = []
for i in range(M):
    features.append(circuit(weights, X[i]))
return np.stack(features)

```

Here, we are creating a _list_ containing the circuit results, and then ‘stacking’ them via `np.stack` to convert it into an array.

There is one more change needed to get it working — we need to replace `array.conj()` with `np.conj(array)` (this former is another NumPy feature seemingly not supported by Autograd). With these two changes, the script now works:

```python
import pennylane as qml
from pennylane import numpy as np
from pennylane.init import qaoa_embedding_uniform
from pennylane.templates import QAOAEmbedding

n_qubits = 5
n_layers = 2

dev = qml.device("default.qubit", wires=n_qubits)

@qml.qnode(dev, diff_method="backprop")
def circuit(weights, feature):
    QAOAEmbedding(features=feature, weights=weights, wires=range(n_qubits))
    return qml.state()

weights = qaoa_embedding_uniform(n_layers, n_qubits)

N = 10
d = 4
X = np.random.uniform(size=(N, d))

# map x to quantum state |x>
def encoder(weights, X):
    M = X.shape[0]
    features = []
    for i in range(M):
        features.append(circuit(weights, X[i]))
    return np.stack(features)

# kernel matrix
def matrix(features):
    # <x_i|x_j>
    t1 = features @ np.conj(features).T
    # |<x_i|x_j>|^2
    t2 = np.multiply(t1, np.conj(t1))
    return np.absolute(t2)

def cost_naive(weights, X=None):
    features = encoder(weights, X)
    K = matrix(features)
    return K.sum()

optim = qml.AdamOptimizer()
for i in range(10):
    weights, loss = optim.step_and_cost(cost_naive, weights, X=X)
    print(weights[0])

```

Let me know if that works for you, or if you have any other questions!

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<div class="post-metadata">

**Author:** ![Zedd](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/zedd/32/2164_2.png) [@Zedd](https://discuss.pennylane.ai/u/Zedd)\
**Post date:** [March 16, 2021, 11:58am UTC](https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920/3 "2021-03-16T11:58:42Z")

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Wow, thank you @josh, it works. And thanks for explaining it in every detail.

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<div class="post-metadata">

**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:** [March 16, 2021, 12:22pm UTC](https://discuss.pennylane.ai/t/optimize-with-qml-state-and-autograd/920/4 "2021-03-16T12:22:09Z")

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No worries @Zedd 🙂