updated hhl

[roie-d-classiq]

PR Description

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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[TomerGoldfriend]

Move the link for condition number to the right place.

Correct latex for |vecb|.

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[roie-d-classiq]

Corrected the reference, didn't quite understand what was the problem with the latex?

[TomerGoldfriend]

registers --> variables

\tilde{lambda}_j are the m bit approximations (correct n to m).

What is s?

C=1/2^m (correct n to m).

Maybe comment here that in principle, when \lambda-s do not have an exact m-binary representation, then there is also garbage for $|lambda \neq 0\rangle |1\rangle$.

You work here with the names memory and estimator, but in the code you use different namings. Maybe it is better to choose on wording, but I am not sure...

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[roie-d-classiq]

modifed registers. Note that this is a very common term in the literature on quantum algorithms.

s is the sparsity of A, added a definition.

You're right, for a second it seemed weird to me that the minimum eigenvalue would depend on the phase accuracy, but now I see what is happening.

I'll modify the code accordingly.

[TomerGoldfriend]

Maybe we can remove this? The algorithm has 5 steps as written in the introduction.

Why the first step of preparing b deserves a subsection of its own, while all the other steps are given in a single block?

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[roie-d-classiq]

For sure, I deleted the headline of the subsection

[TomerGoldfriend]

", returning a normalized solution" - I do not think this is actually the case here, since you do not do the final step of post-selecting ind=1.

which indicates the powers --> which indicates how the powers

number of phase qubits = m

 and indicates if the phase qubits return a normalized solution - I did not understand this sentence, how is it related to the phase qubits.

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[roie-d-classiq]

Yes, I agree, fixed it.

[TomerGoldfriend]

The ambiguity is resolved by isolating the global phase. -- which ambiguity?

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[roie-d-classiq]

The ambiguity in the phase..., modified the sentence

[roie-d-classiq]

In the following section I modified the code..., this code was ori's version, I replaced it with my code performing the global phase identification using the scalar product....

[TomerGoldfriend]

We will define the inner quantum call to be used within the flexible QPE: a Suzuki Trotter of order one [3], whose repetitions parameter grows by some constant factor proportional to the evolution coefficient.

--> I think you repeat the info of this paragraph in the following paragraph.

estimator size m

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[roie-d-classiq]

yes, fixed

[TomerGoldfriend]

We can replace the sparsity condition on A by any --> unfinished sentence.

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[roie-d-classiq]

We can replace the sparsity condition on $A$ by any restriction allowing efficient Hamiltonian simulation.

Fixe the sentence

[TomerGoldfriend]

Remove # from the title text

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[roie-d-classiq]

weird, I don't see it..., it looks all right in my version

[github-actions]

🔥 Great job, @roie-d-classiq! You've merged your 6th PR! 🎊

Your contributions to classiq-library are making a real difference. Keep up the fantastic work! 💪
Remember, every PR counts and helps improve the project. What will you tackle next? 🤔