# Is there a calculation error in "Circuits as Fourier series" PennyLane Demo?

**URL:** <https://discuss.pennylane.ai/t/is-there-a-calculation-error-in-circuits-as-fourier-series-pennylane-demo/4005>\
**Category:** PennyLane Help\
**Created:** [January 31, 2024, 8:30pm UTC](https://discuss.pennylane.ai/t/is-there-a-calculation-error-in-circuits-as-fourier-series-pennylane-demo/4005 "2024-01-31T20:30:53Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![doktrster](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/doktrster/32/2269_2.png) [@doktrster](https://discuss.pennylane.ai/u/doktrster)\
**Post date:** [January 31, 2024, 8:30pm UTC](https://discuss.pennylane.ai/t/is-there-a-calculation-error-in-circuits-as-fourier-series-pennylane-demo/4005/1 "2024-01-31T20:30:53Z")

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My question is about this article:

> **[Circuits as Fourier series | PennyLane Demos](https://pennylane.ai/qml/demos/circuits_as_fourier_series/)**
>
> Learn with this interactive, code-free introduction to the idea of quantum circuits as Fourier series.

Is there a calculation error here:

 ![изображение_2024-01-31_230419712](https://canada1.discourse-cdn.com/flex012/uploads/pennylane/original/2X/6/61fe769454d86e9674d589ee027efbb9c54590af.png)

I used Euler’s formula for T\_{s} - T\_{-s} elements and got this:

D = \frac{\gamma}{sin{(2\gamma s)}} (T\_{s} - T\_{-s})

And the same is for the derivative:

f'(\theta) = \frac{\gamma}{sin{(2\gamma s)}}[f(\theta + s) - f(\theta - s)]

Am I wrong or not?

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**Author:** ![isaacdevlugt](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/isaacdevlugt/32/1159_2.png) [@isaacdevlugt](https://discuss.pennylane.ai/u/isaacdevlugt)\
**Post date:** [January 31, 2024, 11:35pm UTC](https://discuss.pennylane.ai/t/is-there-a-calculation-error-in-circuits-as-fourier-series-pennylane-demo/4005/2 "2024-01-31T23:35:15Z")

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Hey @doktrster! Welcome to the forum 🙂

I’ve contacted the author of the demo to make sure I get this right. We’ll get back to you as soon as we can!

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**Author:** ![David\_Wakeham](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/david_wakeham/32/1515_2.png) [@David\_Wakeham](https://discuss.pennylane.ai/u/David_Wakeham)\
**Post date:** [February 2, 2024, 6:38pm UTC](https://discuss.pennylane.ai/t/is-there-a-calculation-error-in-circuits-as-fourier-series-pennylane-demo/4005/3 "2024-02-02T18:38:47Z")

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Hi doktrster! Yep, that looks like a typo 😅 Thanks for spotting it!