Methods for calculating expectation values from a list of observables, sampling from final state.

[sebgrijalva]

Changes:

• Simulation.run() only evaluates the states at each time
• Simulation.run() outputs a list of numpy.ndarray vectors instead of qutip.Qobj
• To obtain expectation values, a new method Simulation.expect() allows for a list of observables to be provided, then uses the states at each time step to show the evolution of the observables.
• A new method, Simulation.sample_final_state() returns a collections.Count dictionary with a chosen number of samples from the final state of evolution.

The notebooks have been adapted to reflect these proposed changes.

This also in reference to #55 and #56

[sebgrijalva]

Comments/Reviews are very welcome, @HGSilveri , @LucasGitQ @cdalyac

[HGSilveri]

Here are some remarks and potential improvements.

I still think these methods would fit better in a dedicated SimulationResults class, which would be the output of Simulation.run().

[lhenriet]

Ah I remark that one of my comments on N was also pointed out by Henrique. The fix still does not address the 2-level nature of the measurement vs the (occasional) 3-level nature of the system.

[HGSilveri]

Ah I remark that one of my comments on N was also pointed out by Henrique. The fix still does not address the 2-level nature of the measurement vs the (occasional) 3-level nature of the system.

You're right, I forgot about this. It also reminds me that we choose the measurement basis in Sequence, which will influence the results here. Do you want me to take a look at this @sebgrijalva ?

[sebgrijalva]

I will open a new issue for this three-state measurement. For the moment, the sampling method will only work for two-state measurement.

[lhenriet]

A minor edit that you can maybe put in this pull request. Now that we have the interaction_coeff and rydberg_blockade_radius in device, I think we can safely suppress self._U. What do you think ?

[sebgrijalva]

Yes, I forgot about that, thank you.

[sebgrijalva]

Thanks, this is looking pretty good. One question: normally one would declare a measurement basis in the sequence (by adding a seq.measure() Timeslot). This basis name is then stored in Sequence._measurement (which so far is private). Then, when calling the method in SimulationResults.sample_final_state, it would read the instruction from the sequence. What do you think about this order of steps?

[HGSilveri]

I thought about this. The downsides are that it requires making and simulating a new sequence to change the measurement basis and that it might be confusing when you're not sampling, as having a measurement at the end of a Sequence can be equated to a projection of the state vector. When you're interested in the full state vector, I would lean towards a sequence without a measurement.

That being said, perhaps we can make meas_basis a keyword argument meas_basis=None, which when left as None would take the measurement basis from the Sequence. If the Sequence didn't have one, it would throw an error asking for the meas_basis explicitly. What do you think?

[sebgrijalva]

That being said, perhaps we can make meas_basis a keyword argument meas_basis=None, which when left as None would take the measurement basis from the Sequence. If the Sequence didn't have one, it would throw an error asking for the meas_basis explicitly. What do you think?

I think this is a good solution, meas_basis as a kwarg gives both options.

[sebgrijalva]

So how is this looking now? Can we merge so that the notebooks in (optimal_control and MIS) can be adapted?

[HGSilveri]

I'll do another review.

[HGSilveri]

Looking good overall. After you address these remarks, it should be okay to merge on my end.

[lhenriet]

It looks good to me.

[HGSilveri]

nit: needs a tab

[HGSilveri]

Other than that nit, it looks good to me!