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Hamiltonian simulation guide #201

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merged 6 commits into from
Aug 16, 2024

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alexandre-ricardo
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Adding a first draft for the Hamiltonian Simulation guide. Not yet finished.

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@alexandre-ricardo alexandre-ricardo marked this pull request as draft July 10, 2024 11:50
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@TomerGoldfriend TomerGoldfriend Jul 27, 2024

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Maybe mention that given a Suzuki-Trotter formula, there are exponential different ways to implement it. The synthesis engine generates an optimized implementation, reducing CX-counts and depth compared to a naive, non-optimized implementation.


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@TomerGoldfriend TomerGoldfriend Jul 27, 2024

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and apply it ---> and applies it


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@TomerGoldfriend TomerGoldfriend Jul 27, 2024

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Line #10.            num_qdrift=30,

why did you choose 30? is it according to the error formula you have written above?


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@TomerGoldfriend TomerGoldfriend Jul 27, 2024

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Nice plot. I would increase num_qdrift , or, alternatively, use num_qdrift=30 as you did but run the simulation several times to get some statistics (this is eventually a random approach). You can use ExecutionSession .


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@TomerGoldfriend TomerGoldfriend Jul 27, 2024

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The notebook in the link shows two things:

  1. How to use these methods for Hamiltonian derived from molecules.
  2. The optimization of these functions by the synthesis engine.

I am not sure it gives more experience, it mainly highlights the latter (which is a good thing to mention).


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@alexandre-ricardo alexandre-ricardo marked this pull request as ready for review July 31, 2024 17:43
@EdenSchirmanClassiq
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@alexandre-ricardo Great tutorial! Super insightful and concise, well done!

A few notes that we will speak in our meeting:

  • At the beggining, add: Additiona methods of QSVT and ... are briefley stated and referenced.
  • Trotterization
  • 1st order general, 2nd order example - I would go with the general and the simplest example in both. Or just general, and the in the example to cover the 1st and 2nd order examples.
  • Evolution coefficient - explanation, how to choose
  • Exponentiation with depth constraint
  • depth of the circuit?
  • can we extract the order?
  • qdrift
  • The 3 dots I would explain the algorithm a bit more
  • Block encoded HAmiltonians
  • A bit more explanations. Why necessity?
  • qubitization: why only walk operator?
  • Example
  • Why '11' different case? add comment..
  • qdrift - haven't you said something statistical?
  • Exercise, I'm not sure I understood - to apply the methods for the tutorial?
  • I like the idea of a molecule, I would do estimation of some interesting operator at different times.

@EdenSchirmanClassiq EdenSchirmanClassiq self-requested a review August 16, 2024 12:04
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Great

@EdenSchirmanClassiq EdenSchirmanClassiq merged commit a27fdb4 into Classiq:main Aug 16, 2024
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3 participants