Library/arielsmoler/cad 25376/add solving qlsp with aqc notebook

[arielsmoler]

PR Description

Some notes

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

• And that the files have indicative names.

• Please note that Classiq runs automatic code linting, which may minorly alter some files.

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[orsa-classiq]

*with - typo

[orsa-classiq]

Also I wouldn't call it 'Part 1'. In the IDE I would give it a stand-alone name. Maybe 'naive' or 'linear scheduling' or 'trotterization' etc

[arielsmoler]

Good catch

[orsa-classiq]

type in the filename
vqls -> qlsp

[arielsmoler]

for sure1

[orsa-classiq]

"(see our AQC tutorial)." -> put a link to the tutorial

"2.1 Null Space of H0" -> contructing H0?

"bounded below by 1/k" -> bounded from below by 1/k. (maybe write each one of them in the previous sections instead here?). Don't forget to remove 'VERIFY'

maybe explain what is the Null space (in a few words, like: in the Null space, i.e. has eigenvalue 0)

"There exists a state " -> maybe there exist an additional state. I would explain that unlike the regular adiabatic algo usages, here this is not the ground state, and also there is a degeneracy in the number of states. The authors prove that if we start in the eigenstate |x> and evolve slowly enough, we will remain in this eigenstate path

Reply via ReviewNB

[arielsmoler]

edited

[orsa-classiq]

Line #45.        HO_HAMILTONIAN = matrix_to_hamiltonian(H0)

I think that it is possible to use the prepare_state(b) to directly encode the exp(iH0*t) by using the phase operator, like the grover-diffuser, and the projector_controlled_phase operation in the qsvt.

You do something like:

A*B_dag*phase(t)*B*A_dag

where A = inplace_prepare_state(b, qvar)

B = aux = (qvar == 0)

phase(t) = phase(aux, t)

like:

within_apply(lambda: [inverse(inplace_prepare_state(b, 0, qvar),
                      assign(qvar==0, aux)],
             lambda: phase(aux * t, 1))

Reply via ReviewNB

[TomerGoldfriend]

Cool!! @orsa-classiq

[arielsmoler]

this is super interesting!! and actually quite impressive - i tried to work my way through it but u will be happy to get a better understanding as it looks brilliant

[orsa-classiq]

I would also add a zoom-in picture to the y values [-1.3, 1.3]

Reply via ReviewNB

[arielsmoler]

added :)

[orsa-classiq]

something parsed wrong with the $ signs in the first line (maybe its just the review-nb)

Reply via ReviewNB

[arielsmoler]

see what you mean - i think its only the ReviewNB

[orsa-classiq]

Line #39.        # Calculate phase difference

I don't understand this measure. Phase difference is acceptable as QC is always up to a global phase

Reply via ReviewNB

[arielsmoler]

correct. it was for my own sake to see that ther is "only" a global phase difference as the states seemed different but the similarity was high. removed it

[orsa-classiq]

Line #43.    

redundant lines

Reply via ReviewNB

[orsa-classiq]

Line #2.    # Use np.linalg.solve() to find x

redundant comment, does not add information to the next line

Reply via ReviewNB

[arielsmoler]

removed

[orsa-classiq]

I would write here \ in the complexity part what we did here that was not optimal. e.g suzuki-trotter instead of dyson, non-optimal schedule function, brute-force encoding of the pauli-operators (which scale exponentially)

Reply via ReviewNB

[arielsmoler]

good point. added

[TomerGoldfriend]

Maybe comment that this is a purely mathematical pre-process. That you do it here exact, however, in real life probably the condition number will be approximated somehow, or known in advance from some external considerations.

Reply via ReviewNB

[arielsmoler]

added

[TomerGoldfriend]

I would put all the equations in the appendix (Technical details) and put here only the bottom line (with referring to the "Technical Details" section):

The formula shows that the adiabatic error is minimized when:

1. 
   
2. 
   
3. 
   

Reply via ReviewNB

[arielsmoler]

great idea! done

[TomerGoldfriend]

cab --> can

Reply via ReviewNB

[arielsmoler]

:)