# Data encoding in CV setting

**URL:** <https://discuss.pennylane.ai/t/data-encoding-in-cv-setting/582>\
**Category:** PennyLane Help\
**Created:** [September 24, 2020, 10:11am UTC](https://discuss.pennylane.ai/t/data-encoding-in-cv-setting/582 "2020-09-24T10:11:07Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![valeria](https://avatars.discourse-cdn.com/v4/letter/v/48db29/32.png) [@valeria](https://discuss.pennylane.ai/u/valeria)\
**Post date:** [September 24, 2020, 10:11am UTC](https://discuss.pennylane.ai/t/data-encoding-in-cv-setting/582/1 "2020-09-24T10:11:08Z")

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Hi,

I would like to better understand how data encoding is performed in the CV setting. In [https://pennylane.ai/qml/glossary/quantum\_embedding.html](https://pennylane.ai/qml/glossary/quantum_embedding.html) I read that with continuous variable quantum computing models we usually use Squeezing and Displacement embeddings, so I would like to focus on them.

For **Squeezing encoding** , I know from [https://arxiv.org/abs/1803.07128](https://arxiv.org/abs/1803.07128) that we start from the decomposition of a squeezed state in the Fock basis  
|z\>=\frac{1}{\sqrt{\cosh r}}\sum\_{n=0}^{\infty}\frac{\sqrt{(2n)!}}{2^nn!}(-e^{i\varphi}\tanh r)^n|2n\>,\qquad z=re^{i\varphi},  
and using the _squeezing feature map with phase encoding_ \phi:|x\>\to|(c,\boldsymbol x)\>, we get the kernel  
\kappa(\boldsymbol{x},\boldsymbol{x'};c)=\prod\_{i=1}^{N}\<(c,x\_i)|(c,x\_i')\>, with \<(c,x\_i)|(c,x\_i')\>=\sqrt{\text{sech}(c) \text{ sech}(c)}\sum\_{n=0}^{\infty}\frac{(2n)!}{2^{2n}n!^2}(e^{i(x\_i'-x\_i)}\tanh c\tanh c)^n=  
\sqrt{\frac{\text{sech} (c)\text{ sech} (c)}{1-\exp(i(x'\_i-x\_i)\tanh c\tanh c)}}, where c is the squeezing strength.

My question is about **Displacement encoding** instead: we know that the decomposition of a coherent state in Fock basis is  
|\alpha\>=e^{-|\alpha|^2/2}\sum\_{n=0}^{\infty}\frac{\alpha^n}{\sqrt{n!}}|n\>, \alpha\in\mathbb{C}. What kind of feature map should we use in this case? What is the resulting kernel?

Thanks in advance!

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**Author:** ![Nicolas\_Quesada](https://yyz2.discourse-cdn.com/flex012/user_avatar/discuss.pennylane.ai/nicolas_quesada/32/118_2.png) [@Nicolas\_Quesada](https://discuss.pennylane.ai/u/Nicolas_Quesada)\
**Post date:** [September 24, 2020, 1:54pm UTC](https://discuss.pennylane.ai/t/data-encoding-in-cv-setting/582/2 "2020-09-24T13:54:43Z")

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Hi Valeria — For the displacement encoding you end up with a Gaussian kernel, since |\langle \alpha| \beta \rangle| \sim \exp(\frac12 |\alpha - \beta|^2).

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**Author:** ![valeria](https://avatars.discourse-cdn.com/v4/letter/v/48db29/32.png) [@valeria](https://discuss.pennylane.ai/u/valeria)\
**Post date:** [September 24, 2020, 2:47pm UTC](https://discuss.pennylane.ai/t/data-encoding-in-cv-setting/582/3 "2020-09-24T14:47:25Z")

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Thanks a lot @Nicolas_Quesada !