Qiskit-terra: Support for `Parameter`s with complex values

[lcapelluto]

What is the expected enhancement?

Parameters are now used in schedules. Schedules have pulses which may have complex amplitudes. I'd like to be able to do this:

from qiskit import pulse
from qiskit.circuit import Parameter

amp = Parameter('amp')
sched = pulse.Schedule()
sched += pulse.Play(pulse.Gaussian(duration=128, sigma=16, amp=amp),
                    pulse.DriveChannel(0))
sched.assign_parameters({amp: 0.2j})

[paniash]

Hey! I'd like to work on this.

[taalexander]

Excellent, @paniash! I've assigned. Please feel free to ask about any questions you may have 😄 .

[paniash]

Thanks a lot! Will do! :)

[paniash]

@taalexander Just wanted to clarify something. In the current master branch, pulse supports pulse.Schedule.assign_parameters() but only real amplitudes. The enhancement is to include complex amplitudes as well. Am I right?

[Arijit02]

Hey! Is this issue open? Can I check this out?

[paniash]

@Arijit02 Hey! Thanks for your interest but I'm currently working on it. :)

[Arijit02]

Okay, fine.

[lcapelluto]

@paniash, the changes will mostly be in circuit/parameterexpression.py. There will likely be a couple changes required in pulse/ once complex values are supported, but that can be done in a separate PR after this issue is completed. If you run the short snippet from the description, I believe the error is raised in _raise_if_passed_non_real_value in ParameterExpression

[eggerdj]

Will this also allow us to do things like below?

beta = Parameter('β')
1.0j*beta

[Cryoris]

I actually implemented this before for personal use but never opened a PR because I couldn't find a use-case for it. @paniash looking at the early stage of your PR it might be best if I open one and you can help contribute if there's something left, what do you think? 😄
Complex parameters should also include some validation to not end up with expressions such as RY(0.2j) which will crash the execution.

[paniash]

@Cryoris I'd be glad to! Given my knowledge of python, I don't want to be a bottleneck to merge this PR, so by all means, go ahead. I'm willing to contribute any missing pieces, if present, to your PR.

P.S. Should I close my PR then? Maybe @lcapelluto could confirm.