# Numpy says "probabilities do not sum to 1"
**URL:** https://discuss.pennylane.ai/t/numpy-says-probabilities-do-not-sum-to-1/487
**Category:** PennyLane Help
**Created:** [July 21, 2020, 2:16am UTC](https://discuss.pennylane.ai/t/numpy-says-probabilities-do-not-sum-to-1/487 "2020-07-21T02:16:45Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@snuffkin](https://discuss.pennylane.ai/u/snuffkin)
#### Post date: [July 21, 2020, 2:16am UTC](https://discuss.pennylane.ai/t/numpy-says-probabilities-do-not-sum-to-1/487/1 "2020-07-21T02:16:45Z")
Hi!
I resize the MNIST images to 16x16 and run a quantum circuit.
If I use AmplitudeEmbedding and set `analytic=False`, I get a numpy error.
I assume this is a probability accuracy issue.
[mnist\_20200721\_numpy\_error.txt](https://discuss.pennylane.ai/uploads/short-url/rH1wv4kID5gWDzzlqhg3eOlr4h6.txt) (31.6 KB) → Please change the file extension to “ipynb”.
Is there a workaround?
error message:
```
ValueError: probabilities do not sum to 1
```
---
### Author:  [@Maria\_Schuld](https://discuss.pennylane.ai/u/Maria_Schuld)
#### Post date: [July 21, 2020, 8:46am UTC](https://discuss.pennylane.ai/t/numpy-says-probabilities-do-not-sum-to-1/487/2 "2020-07-21T08:46:15Z")
Hey snuffkin!
You uncovered a very interesting bug there!
What seems to happen is that the conversion from tf tensors to numpy arrays creates an `ndarray` of data type `float32`. I suspect that with this lower precision, the automatic normalisation of the `AmplitudeEmbedding` method creates a quantum state vector which does not pass the checks of numpy’s `np.random.choice` (which is used for sampling measurement results in `"default.qubit"`) for a probability distribution to be normalised.
As a fix, you’d need to convert your array to `float64`:
```python
n_qubits = 8
dev = qml.device("default.qubit", wires=n_qubits, shots=10, analytic=False)
# quantum circuit
@qml.qnode(dev)
def circuit(features=None):
qml.templates.AmplitudeEmbedding(features, range(n_qubits), normalize=True)
return qml.expval(qml.PauliZ(0))
circuit(features=x_train[0].flatten().astype('float64'))
```
Interestingly, at least for the latest PL version I tested this with, assigning the training data point to a new variable seems to do the conversion automatically.
```python
n_qubits = 8
dev = qml.device("default.qubit", wires=n_qubits, shots=10, analytic=False)
x = x_train[0].flatten()
print(x.dtype) # 'float64'
# quantum circuit
@qml.qnode(dev)
def circuit(features=None):
qml.templates.AmplitudeEmbedding(features, range(n_qubits), normalize=True)
return qml.expval(qml.PauliZ(0))
circuit(features=x)
```
Hope this helps!
---
### Author:  [@snuffkin](https://discuss.pennylane.ai/u/snuffkin)
#### Post date: [July 21, 2020, 1:04pm UTC](https://discuss.pennylane.ai/t/numpy-says-probabilities-do-not-sum-to-1/487/3 "2020-07-21T13:04:11Z")
Hi @Maria_Schuld,
Thanks for your response!
With your support, my program works.
PennyLane is easy to use and fun to use.