8000 PurificationMPS from density matrix · Issue #501 · tenpy/tenpy · GitHub
[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to content

PurificationMPS from density matrix #501

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom
Closed
victorbayonamarchal opened this issue Apr 22, 2025 · 3 comments
Closed

PurificationMPS from density matrix #501

victorbayonamarchal opened this issue Apr 22, 2025 · 3 comments
Labels
enhancement New feature or request

Comments

@victorbayonamarchal
Copy link

Hello!
I was wondering if there is already a way of building a PurificationMPS from a dense density matrix (mixed states). I have worked through the different ways of building PurificationMPS in the documentation but I don't see how can I build this from a density matrix.
Thank you!
@victorbayonamarchal victorbayonamarchal added the enhancement New feature or request label Apr 22, 2025
@Jakob-Unfried
Copy link
Member
Jakob-Unfried commented Apr 23, 2025 •
edited
Loading

You can use PurificationMPS.from_full if you have the full wavefunction of a purification of your density matrix.
And you should be able to get that e.g. as the vectorization of $U \sqrt{D}$, where $\rho = U D U^\dagger$ is the eigendecomposition of the density matrix. Note that $D \geq 0$ if $\rho$ is a density matrix.

For the "vectorization" you essentially dont need to do anything in the numerics. If we have $\rho$ with legs p0, ..., pN, p0*, ..., pN*, then $U \sqrt{D}$ with the same legs is a state in the doubled Hilbert space by identifying legs pi* as qi. Just make sure the open legs of $U$ end up as phyiscal legs and the open legs of $\sqrt{D}$ as ancillas.

Feel free to re-open if you run into problems.

@Jakob-Unfried
Copy link
Member

If you end up coding this, consider contributing with a PR =)

@Jakob-Unfried
Copy link
Member
Jakob-Unfried commented Apr 23, 2025 •
edited
Loading

Note that I recently fixed from_full to actually work with PurificationMPS.

This is not yet part of the most recent release, so to get it immediately, you need to install tenpy from source.
We should probably do another release soon, its been a while
The fix is part of v1.0.6

This was referenced Apr 25, 2025
Closed
Open
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Assignees
No one assigned
Labels
enhancement New feature or request
Projects
None yet
Milestone
No milestone
Development

No branches or pull requests
2 participants
@Jakob-Unfried @victorbayonamarchal
0