AQC-Tensor tutorial is hard to follow because there are too many circuits

[kevinsung]

URL to the relevant tutorial

https://quantum.cloud.ibm.com/docs/en/tutorials/approximate-quantum-compilation-for-time-evolution

Select all that apply

• new content request
• typo
• code bug
• out-of-date content
• broken link
• other

Describe the fix or the content request.

It has these circuits:

• aqc_target_circuit
• subsequent_circuit
• aqc_comparison_circuit
• reference_circuit
• aqc_good_circuit

Some suggestions:

• reference_circuit is unnecessary. We can should just compute the exact time evolution directly as expm(-i H t)
• We could remove subsequent_circuit
• We could remove aqc_comparison_circuit

For new content requests - if the request is accepted, do you want to write the content?

I will write (or already have written) a draft of the proposed content

[miamico]

@kevinsung are you sure we can remove reference_circuit? in the second part of the notebook we have a large scale example and you can't directly take the exponential of H

[kevinsung]

@kevinsung are you sure we can remove reference_circuit? in the second part of the notebook we have a large scale example and you can't directly take the exponential of H

True, I hadn't thought of the second part. Still, it seems undesirable from a pedagogical point of view to introduce an arbitrary-seeming number of Trotter steps (200) to represent the "exact" evolution. How do we know 200 is enough? The reader just has to believe it, and also remember the difference between that Trotter step number and the other ones in the tutorial.

Perhaps for the second part, we can choose parameters of the Heisenberg model that cause it to be exactly solvable (for example, by mapping to free fermions). Besides this, I don't have any good suggestions.

[miamico]

Ok, that sounds more work than a simple drop-in replacement for that edit. Let's keep this on the radar to maybe revamp the tutorial