N-body rotations #117

fangzh-umich · 2017-12-01T15:55:52Z

Resolves issues #86 and #116.

I implemented general n-body rotations of PolynomialTensor using np.einsum, with the option optimize = True to ensure that we trade space for time (e.g. in the 2-body term, use the O(N^5) algorithm instead of the O(N^8) one).

Also, as per issue #116, @kevinsung and I changed the convention for the rotation matrix so that it's consistent with the release paper.

…o n_body_rotations Now the module and the test both use the convention in the paper

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fangzh-umich · 2017-12-01T16:03:13Z

OK, I signed it.

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kevinsung · 2017-12-01T16:09:47Z

src/openfermion/ops/_polynomial_tensor.py

+    """Change the basis of an general interaction tensor.
+
+    M' = R^T.M.R where R is the rotation matrix, M is the general tensor
+    and M' is the transformed general tensor.


Should it be R.M.R^T? Also, perhaps there is a better way to express what this does, as transpose seems to me to be a 2-d concept; I might be wrong.

It's a rotation "matrix", of course it's 2-d.

kevinsung · 2017-12-01T16:12:25Z

src/openfermion/ops/_polynomial_tensor.py

+    # "optimize = True" does greedy optimization, which will be enough here
+    transformed_general_tensor = numpy.einsum(subscripts,
+                                              general_tensor,
+                                              *rotation_matrices,


What does the * in *rotation_matrices do?

It's a Python syntax to pass a variable number of parameters to a function. For example, if key is (0,0,0) then this is equivalent to numpy.einsum(subscripts, general_tensor, rotation_matrix, rotation_matrix, rotation_matrix).

kevinsung · 2017-12-01T16:14:52Z

For testing, perhaps we can compute the rotated matrix in two different ways, one using your new function, and another using a naive sum, like Eq. (22) in the paper, and make sure they match up? It doesn't seem like a great test but I can't think of a better way right now.

Perhaps the functions one_body_basis_change and two_body_basis_change should be removed completely?

Yes, of course I'm okay with my commits being used in this PR.

fangzh-umich · 2017-12-01T16:18:41Z

I'm not sure how to increase the coverage of my test.

First, there is a maximum order restriction because of a limitation of numpy.einsum: it uses letters to indicate subscripts, and there are only 52 (upper case and lower case) in the English language. I don't expect anyone to actually hit it, and I hope a future version fixes this (probably when numpy itself overcomes this limitation).

Second, my code has no use for one_body_basis_change and two_body_basis_change, but I left them in because __init__.py explicitly imports those functions. I don't know what those imports are for, so I didn't just remove them.

kevinsung · 2017-12-01T16:37:29Z

Ok then, this looks good to me after you address the "R.M.R^T" thing.

Now the comment better expresses the general algorithm.

fangzh-umich · 2017-12-01T18:00:25Z

Actually, my test just showed that numpy complains about "too many subscripts in einsum" before it gets to 26 52 indices.

fangzh-umich · 2017-12-01T18:08:01Z

Also, I realized that you defined PolynomialTensorError, but you never raised it, and you never exported it (meaning that it's not visible to the user). Since my code raised that exception, I exported it.

But am I supposed to raise some other exception like ValueError? What is the intended use of PolynomialTensorError?

fangzh-umich · 2017-12-01T18:17:30Z

I'm still not sure what I should do with one_body_basis_change and two_body_basis_change. Should I unexport them or should I test them? Should I export my general_basis_change too?

kevinsung · 2017-12-01T18:33:49Z

Don't export PolynomialTensorError, and raise a ValueError instead.

I think we should remove one_body_basis_change and two_body_basis_change, and also not export general_basis_change. I don't see any reason general_basis_change needs to be exposed to users, but somebody else (maybe @babbush ) should have the final say on that.

I don't know what to say about einsum complaining before there are 26 indices.

babbush

This mostly looks good, thanks for the contribution. Feel free to add yourself to the alphabetical part of the credits in the NOTICE and the README.

babbush · 2017-12-01T22:25:12Z

src/openfermion/ops/_polynomial_tensor.py

-                                               rotation_matrix)
-    return transformed_one_body_tensor
+    order = len(key)
+    if order > 26:


Where is this order 26 limit coming from? I suggest not having a maximum order restriction.

It comes from using the numpy.einsum function, which uses letters for indices, and there are 26 upper case and 26 lower case in total (and I need two letters for each dimension of the tensor). However, actually numpy complains about "too many subscripts in einsum" before the 26 limit is reached.

I don't think anything more than 16 is useful in any case.

babbush · 2017-12-01T22:29:29Z

src/openfermion/ops/__init__.py

-from ._polynomial_tensor import (PolynomialTensor,
-                                 one_body_basis_change,
-                                 two_body_basis_change)
+from ._polynomial_tensor import PolynomialTensor


we like to have alphabetically organized imports when possible.

Sure, but I didn't introduce this problem. If the person originally writing this code didn't have any particular reason to do it this way, I will change that.

It turns out that I can't change the order freely, because some files imported later depends on some earlier imports having been processed.

babbush · 2017-12-01T22:36:58Z

src/openfermion/ops/_polynomial_tensor.py


-def two_body_basis_change(two_body_tensor, rotation_matrix):
-    """Change the basis of 2-body interaction tensor such as 2-RDM.
+    # 'aA,bB,cC,dD'


Can you add a line or two explaining what is happening here a bit more? I am a little confused.

I'm doing the basis change through a single call of numpy.einsum, which requires constructing a fitting subscript string. For example, for the (1, 1, 0, 0) tensor, I'm doing numpy.einsum('abcd,Aa,Bb,Cc,Dd', general_tensor, rotation_matrix.conj(), rotation_matrix.conj(), rotation_matrix, rotation_matrix).

Although I just realized my comment is incorrect after the convention change. I will fix that, and at the same time try to make it more explicit.

babbush

👍

* added test for diagonalizing quadratic Hamiltonians * Generalized the basis change functions * Changed the test to test with complex rotation matrices * changed transpose convention for one-body rotation * Improved the comment of general_basis_change Now the comment better expresses the general algorithm. * Added test for high-order tensor rotation * Raise ValueError instead of PolynomialTensorError * Removed [one|two]_body_basis_change altogether * Improved the comment for the main procedure * Added name into NOTICE and README

kevinsung and others added 5 commits November 29, 2017 19:25

added test for diagonalizing quadratic Hamiltonians

153d65d

Generalized the basis change functions

e1aba18

Changed the test to test with complex rotation matrices

59615c5

changed transpose convention for one-body rotation

20e1b49

Merge remote-tracking branch 'remotes/kevinsung/n_body_rotations' int…

d12a21d

…o n_body_rotations Now the module and the test both use the convention in the paper

kevinsung reviewed Dec 1, 2017

View reviewed changes

fangzh-umich added 2 commits December 1, 2017 12:15

Improved the comment of general_basis_change

d65a7d5

Now the comment better expresses the general algorithm.

Added test for high-order tensor rotation

30884fe

fangzh-umich added 2 commits December 1, 2017 13:39

Raise ValueError instead of PolynomialTensorError

c85691e

Removed [one|two]_body_basis_change altogether

94ff3e1

babbush reviewed Dec 1, 2017

View reviewed changes

babbush and others added 3 commits December 1, 2017 14:58

Merge branch 'master' into n_body_rotations

afae273

Improved the comment for the main procedure

de328aa

Added name into NOTICE and README

314e15d

babbush approved these changes Dec 3, 2017

View reviewed changes

babbush merged commit 98355c6 into quantumlib:master Dec 3, 2017

This was referenced Dec 3, 2017

General n-body rotations for PolynomialTensor #86

Closed

Inconsistency in basis transformations between code and paper #116

Closed

fangzh-umich deleted the n_body_rotations branch December 4, 2017 02:35

conta877 mentioned this pull request Jan 4, 2018

possible issue with basis rotation quantumlib/OpenFermion-Psi4#25

Closed

kevinsung mentioned this pull request Jul 31, 2018

rotate_basis should be a pure function #419

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N-body rotations #117

N-body rotations #117

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