Add norm for second quantized Hamiltonian

[soranjh]

Context:
This PR adds functions for computing the 1-norm of a molecular Hamiltonian from the one- and two-electron integrals and eigenvalues of the factorized two-electron integral tensor.

Description of the Change:

Benefits:

Possible Drawbacks:

Related GitHub Issues:

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[codecov]

Codecov Report

Merging #2653 (fd3d632) into resource_estimation_algorithms (0e84772) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@                       Coverage Diff                       @@
##           resource_estimation_algorithms    #2653   +/-   ##
===============================================================
  Coverage                           99.61%   99.61%           
===============================================================
  Files                                 255      256    +1     
  Lines                               20821    20830    +9     
===============================================================
+ Hits                                20741    20750    +9     
  Misses                                 80       80           

Impacted Files	Coverage Δ
pennylane/resources/__init__.py	100.00% <100.00%> (ø)
pennylane/resources/second_quantization.py	100.00% <100.00%> (ø)

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[Jaybsoni]

Looks good Soran! Just a few quick comments:

• Is this quantity differentiable? Could we compute the gradient wrt the one and two electron integral parameters? If this doesn't make sense to do then no worries, otherwise it might be worth adding a unit test to check for
• I imagine this function will not be user facing but mostly used internally in the resource estimation pipeline. If it is user facing, it might be worth adding tests to make sure that if the parameters one, two, eigvals are given in a different framework (autograd or tf arrays) then this function doesn't fail.
• Codecov is complaining about a few lines which still need to be tested. (you can use #pragma no cover to suppress lines you think have been sufficiently tested but still cause errors in Codcov)

[soranjh]

Looks good Soran! Just a few quick comments:

• Is this quantity differentiable? Could we compute the gradient wrt the one and two electron integral parameters? If this doesn't make sense to do then no worries, otherwise it might be worth adding a unit test to check for

Thanks Jay. I am not actually sure about the benefit of making the norm differentiable wrt the input parameters.

• I imagine this function will not be user facing but mostly used internally in the resource estimation pipeline. If it is user facing, it might be worth adding tests to make sure that if the parameters one, two, eigvals are given in a different framework (autograd or tf arrays) then this function doesn't fail.

I tested the function with inputs given as autograd numpy array and tensorflow varibales and it works. I can add such tests but regarding what mentioned above about differentiability, not sure if these tests are still necessary. If they are still useful, I can add them.

• Codecov is complaining about a few lines which still need to be tested. (you can use #pragma no cover to suppress lines you think have been sufficiently tested but still cause errors in Codcov)

hmm, I see a full coverage for norm_df, and do not see codecov complaining. Where is the complain?

[Jaybsoni]

Looks good Soran! Just a few quick comments:

• Is this quantity differentiable? Could we compute the gradient wrt the one and two electron integral parameters? If this doesn't make sense to do then no worries, otherwise it might be worth adding a unit test to check for

Thanks Jay. I am not actually sure about the benefit of making the norm differentiable wrt the input parameters.

• I imagine this function will not be user facing but mostly used internally in the resource estimation pipeline. If it is user facing, it might be worth adding tests to make sure that if the parameters one, two, eigvals are given in a different framework (autograd or tf arrays) then this function doesn't fail.

I tested the function with inputs given as autograd numpy array and tensorflow varibales and it works. I can add such tests but regarding what mentioned above about differentiability, not sure if these tests are still necessary. If they are still useful, I can add them.

• Codecov is complaining about a few lines which still need to be tested. (you can use #pragma no cover to suppress lines you think have been sufficiently tested but still cause errors in Codcov)

hmm, I see a full coverage for norm_df, and do not see codecov complaining. Where is the complain?

Cool, if differentiability isn't a concern then I doubt we need to test it.

Thats weird, when I reviewed it initially there were some inline comments from codecov complaining about some trivial lines of code. I guess if its not complaining now then this should be good to go. 💯

[Jaybsoni]

Looks good !