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regarding the last paragraph, it is not clear enough to me.
For all quantum algorithms the current system sizes does not supply an improvement over the classical algorithms. But it seems you meant a stronger statement. Say you have 1000 qubit system, do you expect to get something that was not possible to calculate on a classical computer? if so, what is the quantum speedup?
I also think you didn't define what is a map, consider doing that
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We discussed. I will rephrase.
Concerning the definition, I wrote in the second paragraph
"A typical quantum map describes a system undergoing free evolution that is periodically “kicked” by a position-dependent force".
I will move it to the first paragraph
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also, I didn't understand the transition from the hamiltonian to the unitary, is it exact or just the troterized version?
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It is exact, because of the delta function. I will write it.
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Line #6. def pspace_evolution(p: QNum):
I think p_space_... and q_space_... is a bit more readable
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Line #7. phase(p**2 / 2, -2 * pi / 2**p.size)
I would write it as a single expression, i.e
phase((-2 * pi / 2**p.size) * p**2 / 2)
same for the qspace_evolution
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I think "observable" is OK here. It is not the typical "observable" word as in quantum measurement. It means here as being able to be observed.
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PR Description
This PR add a new notebook on the quantum sawtooth map, including run on hardware.