VQE tutorial takes too long to run

[frankharkins]

URL to the relevant documentation

https://learning.quantum.ibm.com/tutorial/variational-quantum-eigensolver (tutorials/variational-quantum-eigensolver/vqe.ipynb).

I ran this overnight and it still had not completed. See #1226 for more context.

Select all that apply

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• out-of-date content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

Describe the fix.

Refactor notebook to run in a reasonable time (once the session actually starts).

[javabster]

also becky says:

This tutorial specifies level 3, but it's ignored: https://learning.quantum.ibm.com/tutorial/variational-quantum-eigensolver If this is not a temporary change, then we shouldn't use level 2 or 3.

[abbycross]

Chiming in:
I am running VQE right now on kyiv and it's been going for 73+ minutes. When I ran it on manila (5Q), it completed in about 30.
Editing to add: apparently that's expected, so nevermind :)