[labs.dla 5] All Cartan involutions + Cartan subalgebra #6396
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
|
Hello. You may have forgotten to update the changelog!
|
Qottmann
changed the title
…into structure_constants_dense
Co-authored-by: David Wierichs <david.wierichs@xanadu.ai>
…nnylane into lie_closure_dense
…into structure_constants_dense
Co-authored-by: David Wierichs <david.wierichs@xanadu.ai>
…aneAI/pennylane into structure_constants_dense
dwierichs
reviewed
Dec 9, 2024
|
@dwierichs feel free to push suggestions straight away 👍 |
Co-authored-by: Pietropaolo Frisoni <pietropaolo.frisoni@xanadu.ai>
dwierichs
approved these changes
Dec 11, 2024
mudit2812
pushed a commit
that referenced
this pull request
Dec 13, 2024
Providing dense implementations for all Cartan involutions listed in appendix C of https://arxiv.org/abs/2406.04418 Adds * `recursive_cartan_decomp` function for recursive cartan decompositions with the appropriate basis changes in between * All canonical Cartan involutions working both with dense and operator representations * `cartan_subalgebra` function to compute the Cartan subalgebra (CSA), i.e. the maximal Abelian subalgebra of $\mathfrak{m}$ using the adjoint representation * misc. helper functions Iterative Cartan decomposition: ```python from pennylane.labs.dla import AI, AII, AIII, BDI, CI, CII, DIII, cartan_decomposition, check_cartan_decomp g = list(qml.pauli.pauli_group(3)) # su(8) g = [qml.matrix(_, wire_order=range(3)) for _ in g] k0, m0 = cartan_decomposition(g, AII) print(f"First iteration: {len(k0)}, {len(m0)}") assert check_cartan_decomp(k0, m0) k1, m1 = cartan_decomposition(k0, CI) assert check_cartan_decomp(k1, m1) print(f"Second iteration: {len(k1)}, {len(m1)}") ``` ```pycon First iteration: 36, 28 Second iteration: 16, 20 ``` [sc-76116] --------- Co-authored-by: David Wierichs <david.wierichs@xanadu.ai> Co-authored-by: Pietropaolo Frisoni <pietropaolo.frisoni@xanadu.ai>
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Providing dense implementations for all Cartan involutions listed in appendix C of https://arxiv.org/abs/2406.04418
Adds
recursive_cartan_decompfunction for recursive cartan decompositions with the appropriate basis changes in betweencartan_subalgebrafunction to compute the Cartan subalgebra (CSA), i.e. the maximal Abelian subalgebra ofIterative Cartan decomposition:
[sc-76116]