Implement the Tensor class

[mrossinek]

Summary

This class is designed to unify the usage of tensors throught the stack. It provides a central entry point for the handling of arrays enabling seamless interchange of dense and sparse arrays in any usecase. This is done by implementing this class as an np.ndarray container as described here. At the same time this class can also wrap a sparse.SparseArray (which in turn implements the np.ndarray interface).

Details and comments

I have two major motivators for this proposal:

1. one is explained in more detail in Improve the handling of label_template during SparseLabelOp.from_polynomial_tensor #1032
2. the other one is the implementation of AO-symmetry aware storage containers for 2-body integrals. I already have some prototypes prepared offline which will allow us to handle 1-, 4- and 8-fold symmetric 2-body terms while they can pretend to be fully functional 4-D matrices for the purposes of expanding them into our Hamiltonian terms (WIP code available here). These classes will also allow us to greatly simplify the logic in our FCIDump parser, effectively dealing with Improve FCIDump parser #933.

[coveralls]

Pull Request Test Coverage Report for Build 4148330521

• 197 of 231 (85.28%) changed or added relevant lines in 5 files are covered.
• 3 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.0007%) to 85.934%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit_nature/settings.py	18	23	78.26%
qiskit_nature/second_q/operators/tensor.py	141	170	82.94%

Files with Coverage Reduction	New Missed Lines	%
qiskit_nature/second_q/operators/spin_op.py	1	83.33%
qiskit_nature/second_q/operators/polynomial_tensor.py	2	87.43%

Totals
Change from base Build 4146231983:	-0.0007%
Covered Lines:	17912
Relevant Lines:	20844

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💛 - Coveralls

[ElePT]

Hi! I think I will probably have to take another look at the PR to fully understand the uses of this new class. So far, I only have a question: I assume there is a good reason for this, but I wonder... why did you choose not to wrap Numbers into non-dimensional np.arrays from the start? I feel like this could simplify the code, but I probably don't have clear enough vision of how numpy works in these cases.

[mrossinek]

Hi! I think I will probably have to take another look at the PR to fully understand the uses of this new class. So far, I only have a question: I assume there is a good reason for this, but I wonder... why did you choose not to wrap Numbers into non-dimensional np.arrays from the start? I feel like this could simplify the code, but I probably don't have clear enough vision of how numpy works in these cases.

Thanks for raising this! I am actually no longer aware of why I tried so hard to achieve this.. 🤔 I just pushed a commit to revert this and see how this goes. This is actually what we were already doing in the PolynomialTensor, too 👍

[woodsp-ibm]

In looking at the intent for this with symmetry integrals this looks like a great thing to have to simplify general usage of such in the stack here.

Needs a release note though I think.