# Generate a MPO from MPS

**URL:** <https://itensor.discourse.group/t/generate-a-mpo-from-mps/198>\
**Category:** ITensor Julia Questions\
**Tags:** mpo\
**Created:** [June 9, 2022, 5:53pm UTC](https://itensor.discourse.group/t/generate-a-mpo-from-mps/198 "2022-06-09T17:53:19Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![jisutich](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@jisutich](https://itensor.discourse.group/u/jisutich)\
**Post date:** [June 9, 2022, 5:53pm UTC](https://itensor.discourse.group/t/generate-a-mpo-from-mps/198/1 "2022-06-09T17:53:19Z")

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Hi,

Suppose I have a pure state \ket{\psi}, I can use a MPS to represent it. But I also want to act some non-unitary operators on the density operator \rho\_0 = \ket{\psi}\bra{\psi} so later it will become a mixed state and I want to generate a MPO to represent the initial state \rho\_0. How to convert my MPS state to a MPO?

Specifically, the state \ket{\psi} which I want is just the product state \ket{\uparrow,\dots,\uparrow}.

Thanks.

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**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [June 9, 2022, 6:20pm UTC](https://itensor.discourse.group/t/generate-a-mpo-from-mps/198/2 "2022-06-09T18:20:07Z")

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You can use:

```julia
rho = outer(psi', psi)

```

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<div class="post-metadata">

**Author:** ![jisutich](https://avatars.discourse-cdn.com/v4/letter/j/e79b87/32.png) [@jisutich](https://itensor.discourse.group/u/jisutich)\
**Post date:** [June 9, 2022, 6:29pm UTC](https://itensor.discourse.group/t/generate-a-mpo-from-mps/198/3 "2022-06-09T18:29:21Z")

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Yes it works. Thanks, Matt!