Added custom theta initialization & small refactor

[japanavi]

Added custom theta initialization parameter custom_theta_init: dict[float]. To initialize custom angles, pass a dict of floats with the angle as key, e.g.

maxcut_benchmark.run(custom_theta_init={"beta": 0.5, "gamma": 0.5})

Slightly refactored code to initialize new thetas in main loop, this means we no longer need the method and rounds parameters in MaxCut since we always pass thetas_init.

Also, fixed title issue in optimality gap plot (was missing the f for the fstring).

[rtvuser1]

Method 1 can also use a different number of rounds even if the incoming theta is None. We could assume that the beta and gamma repeat if not explicitly provided for each round.
I think we should restore rounds as an argument to MaxCut and pass it from run(), so we don't lose that flexibility.
I agree that method could be removed, as we would always want to process the theta array., even for method 1.
So the circuit is always the same for either method 1 or method 2

[japanavi]

Re: "Method 1 can also use a different number of rounds even if the incoming theta is None."

• Was this available in the original implementation, or are you asking me to implement it?
  • We didn't pass in a theta for Method 1, so theta was always None

Re: "We could assume that the beta and gamma repeat if not explicitly provided for each round."

• I can implement a feature that uses a different $\beta, \gamma$ for each round, let me know if you want me to.

[rtvuser1]

Re: "Method 1 can also use a different number of rounds even if the incoming theta is None."

• Was this available in the original implementation, or are you asking me to implement it?

  • We didn't pass in a theta for Method 1, so theta was always None

Re: "We could assume that the beta and gamma repeat if not explicitly provided for each round."

• I can implement a feature that uses a different β,γ for each round, let me know if you want me to.

Regarding method 1 ... previously it always created the default because we didn't pass theta in, so it defaulted. I think we want to create the theta default always, even for method 2 if theta = None. This way method 1 and method 2 are the same in that regard. Both accept rounds and an optional custom theta array, but they always create a similar circuit that could have more than one round.

You could implement the multiple betas and gammas, that might change the behavior when more than one round.
The optimizer will need to adjust multiple parameters in that case, which is different from now.
If it gets at all complicated, you might consider doing that in a diff PR.

[rtvuser1]

OK, merging now