Add QuadraticHamiltonian class

[kevinsung]

Summary

Part of #460. Adds a data structure to represent quadratic Hamiltonians.

Details and comments

I have implemented a method _fermionic_op to convert a QuadraticHamiltonian to a FermionicOp. For now, I have kept that method hidden because I'm not sure what general approach we should take to converting between operator types, e.g., whether we want to have instance methods or whether we want to have a functional style like qiskit_nature.fermionic_op(quadratic_hamiltonian)

[coveralls]

Pull Request Test Coverage Report for Build 2109658637

• 124 of 124 (100.0%) changed or added relevant lines in 2 files are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.2%) to 83.532%

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Totals
Change from base Build 2103855677:	0.2%
Covered Lines:	9029
Relevant Lines:	10809

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💛 - Coveralls

[kevinsung]

The CI failure is unrelated to this PR.

      File "/home/runner/work/qiskit-nature/qiskit-nature/test/algorithms/pes_samplers/test_bopes_sampler.py", line 154, in test_vqe_bootstrap
    np.testing.assert_almost_equal(result.energies, ref_energies)

[woodsp-ibm]

The CI failure is unrelated to this PR.

Was just fixed so I updated your branch - should pass now

[mrossinek]

As outlined here we can proceed with this PR.

[kevinsung]

@mrossinek I have addressed all your comments besides the one related to the copyright checker. If needed, I can manually squash my commits into a single one with a 2022 timestamp.

[mrossinek]

I have addressed all your comments besides the one related to the copyright checker. If needed, I can manually squash my commits into a single one with a 2022 timestamp.

Sounds like the copyright should be fine as only the last year is being checked. Please fix CI and then we can progress with merging this 👍

[woodsp-ibm]

This needs a reno release note for this new feature

[kevinsung]

@woodsp-ibm I've added a release note.

[mrossinek]

Just a minor comment, other than that this lgtm 👍

[mrossinek]

I am wondering if we should rename this to to_second_q_op which is inline with the namings in the properties module.
If we (in the future) design a common base class for some matrix container that will likely be the name of this function, avoiding the deprecation of this one.

[kevinsung]

I think the current name is much better because it precisely describes what the method does. to_second_q_op is confusing because QuadraticHamiltonian is already a "second-quantized op" (though not a SecondQuantizedOp). From the perspective of a user trying to discover this method, I think they are more likely to guess the current name.

[kevinsung]

@woodsp-ibm I have addressed your comments. Please take another look.

[woodsp-ibm]

I think you missed the f from the string they now need to be like f"my value {x}" for the vars to be formatted in.

Also although I put the comment in one place for the error message I was meaning it could apply to a number of the error messages in the various checks to show the failing values where that's applicable.

[kevinsung]

@woodsp-ibm Done.