Add Quantum Drude Oscillator Notebook

[king-p3nguin]

PR Description

I added a notebook for solving the quantum Drude oscillator model.

The notebook includes:

• Implementation QDO Hamiltonian with quadratic coupling in classiq
• Demonstration of ground state energy calculation of QDO Hamiltonian using VQE

*This notebook was created during an internship at Classiq Japan

Some notes

• Please make sure that the notebook runs successfully with the latest Classiq version.

• Please make sure that you placed the files in an appropriate folder

  • And that the file names are clear, descriptive, and match the notebook content.
    • Note that we require the file names of .ipynb and .qmod to be unique across this repository.
  • Plus, please make sure that all required files are included: .qmod, .synthesis_options.json, .metadata.json
  • And that images are embedded inside the notebook, not added as external files

• If applicable, please include link to the paper on which the notebook is based, in the notebook itself.

• Please use rebase on your branch (no merge commits)

• Please link this PR to the relevant issue

• Please make sure to run pre-commit when commiting changes

  • If you're using git in the terminal, make sure to install pre-commit via running pip install pre-commit followed by pre-commit install
    • More info at the pre-commit documentation
  • Note that Classiq runs automatic code linting. Meaning that one of the tests verifies the output of pre-commit.
  • Also note that pre-commit may minorly alter some files. Make sure to git add the changes done by pre-commit

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[github-actions]

🔥 New notebook just dropped!

@amir-naveh , @TomerGoldfriend — come check out this shiny new addition to our repo.

[roie-d-classiq]

Excellent intro, well writen.

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[roie-d-classiq]

I would add a formal definition for k (like in the get_rightmost_zero_pos function)

Also, please change the ket and bra to | \rangle and \langle |, since the documentation doesn't support ket and bra.

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[roie-d-classiq]

I would show why one of these is correct by a simple calculation, or omit the print statement.

and add a statement that they are indeed hermitian conjugates (or omit one of them)

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[roie-d-classiq]

It is better to add an assert statement in both m=1 and m=2, the m=1 is clear but in the m=2 it is hard to compare. You can create an object (for example for m=2) x1x2_analytical = ((np.sqrt(3)+2)/4) Pauli.X(0)*Pauli.X(2) + ....

and then assert that x1x2 is close to x1x2_analytical.

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[roie-d-classiq]

Here, it might simplify the derivation to not that a^dagger a is diagonal in the fock basis and then just evaluate |n><n| in term of the Z and I pauli operators

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[roie-d-classiq]

This should be modified to fit the update way to minimize and perform VQE.

If you have any questions, let me know:)

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[roie-d-classiq]

I'm missing a bit of motivation, why are you comparing this?

Is this just a benchmark?

In the beginning you mentioned 3 molecules so it is worth motivating this calculation and emphasis what it infers.

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[roie-d-classiq]

Analyse the results, shortly, and connect it to the calculation above

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[roie-d-classiq]

Explain what this plot implies, and why do we see the results we see...

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[roie-d-classiq]

Again, these results should be explained/analyzed.

In addition, I would add a comparison of the 3 molecules to showcase the many-body dispersion phenomena and exemplify what you say in the beginning "  however, the total force does not simply triple when a third molecule is introduced" this is super interesting and would be really nice to show how the drude model supports this.

The notebook is well written, interesting and clear!

Thanks for the contribution:)

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