Add Continuous-Time Quantum Walk Notebook

[king-p3nguin]

PR Description

I added a notebook for running a continuous-time quantum walk using FMO Hamiltonian.

The notebook includes:

• Implementation FMO Hamiltonian in classiq
• Demonstration of continuous-time quantum walk using FMO Hamiltonian

*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.

[orsa-classiq]

our documentation doesn't parse well the \bra and \ket, so please replace all of the to |...\rangle

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[orsa-classiq]

I am missing something in the big picture - what is the purpose of the quantum walk in this case?

And what quantity are we measuring?

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[roie-d-classiq]

Note, that the Hamiltonian is quadratic, therefore for an initial fermionic gaussian state such as the vaccum state, or any slater determinate state such as a_m^\dagger....a_1^\dagger|vaccum> the dynamics can be solved in polynomial time in the number of qubits on a classical compute (basically be diagonalizing the single electron Hamiltonian h, where H = sum_{n,m} a_m^\dagger h_{mn}a_n).

see for example https://arxiv.org/abs/2111.08343,

In addition, there are quantum methods to perform efficient and exact propagation of a Gaussian fermionic state, when the dynamics is generated by a quadratic Hamiltonian, so there is no need for Trotterization. See for example: https://arxiv.org/abs/1711.05395

[orsa-classiq]

what is the result that you measure?

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[orsa-classiq]

Line #10.        def main(qnum: Output[QNum]):

I think that you can set time_point as a parameter of main. Then you can synthesize just once, and pass time as a parameter to execution every iteration (see Execution Parameters in the docs)

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[orsa-classiq]

Line #12.            suzuki_trotter(

notice that since the number of repetitions stay the same, you loose accuracy with the increase in time.

You can either increase it or explain it in the graph you plot

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[orsa-classiq]

Line #43.        print(duration)

write text before each number to explain it or just remove the prints

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[orsa-classiq]

why did you choose to plot points only on the peaks? It will be more convincing if you have more points \ points on other trends

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[orsa-classiq]

is this the J_mn in your equation?

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[orsa-classiq]

Is H already in qubits or fermionic?

If it is in qubits, so instead of your create_projector function, I think you can use the matrix_to_hamiltonian function.

BTW in this case is the algorithm scalable? because it seems that the input already scales with the exponent of the number of qubits

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[orsa-classiq]

"Since it is difficult to directly execute ..." - I would use another words. Talk about approximating the evolution.

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