Add Clifford.to_circuit and Clifford.copy methods + initialization via circuits

[renatomello]

Checklist:

• Reviewers confirm new code works as expected.
• Tests are passing.
• Coverage does not decrease.
• Documentation is updated.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (0eeb6ae) 100.00% compared to head (6844488) 100.00%.
Report is 6 commits behind head on master.

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  Files           67        68     +1     
  Lines         9588      9764   +176     
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+ Hits          9588      9764   +176     

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[renatomello]

@BrunoLiegiBastonLiegi @AlejandroSopena this should be ready for review (with some urgency) after passing tests

[BrunoLiegiBastonLiegi]

Thanks @renatomello I just finished giving this a first look and it's looking good. I have got just a couple of general comments.
The first one regards the ability to pass a circuit directly to the Clifford object constructor. From my perspective this is somewhat redundant as you can already do that with Clifford.from_circuit() and it's not really adding any additional functionality.
Secondly I wonder whether many of the clifford_utils functions should be moved to the CliffordBackend object. They are extensively making use of the backend through the Clifford object already, at this point they should probably just be part of it and called at need inside of the Clifford.
Finally, why do you need to store the circuit inside of the Clifford object? In general I would like to keep it as light as possible, keeping in mind that at some point we might want to create an abstract Result object from which both this Clifford, the QuantumState, MeasurementOutcomes, CircuitResult and all the possible future outcomes object inherit from.

[renatomello]

Thanks @renatomello I just finished giving this a first look and it's looking good. I have got just a couple of general comments. The first one regards the ability to pass a circuit directly to the Clifford object constructor. From my perspective this is somewhat redundant as you can already do that with Clifford.from_circuit() and it's not really adding any additional functionality.

Redundancy is not necessarily a bad thing. For instance, we have Clifford.from_circuit(circuit) and CliffordBackend.execute_circuit(circuit). The question is what level of redundancy is acceptable and desirable. And to this point, I insist that Clifford(circuit) is the right level of redundancy and adds to UX. In my opinion, Clifford(circuit) is the most natural way of executing a circuit with the Clifford backend from a user's perspective. Moreover, other libraries, e.g. qiskit support this type of initialization, so it's also natural that users will expect us to support the same thing.

Secondly I wonder whether many of the clifford_utils functions should be moved to the CliffordBackend object. They are extensively making use of the backend through the Clifford object already, at this point they should probably just be part of it and called at need inside of the Clifford.

I have no objection to this. However, this sounds like a different PR.

Finally, why do you need to store the circuit inside of the Clifford object? In general I would like to keep it as light as possible, keeping in mind that at some point we might want to create an abstract Result object from which both this Clifford, the QuantumState, MeasurementOutcomes, CircuitResult and all the possible future outcomes object inherit from.

You are right that it can be memory intensive to store the circuit.queue in the Clifford object. I will roll that back.

[AlejandroSopena]

Thanks @renatomello, everything looks good. I agree with @BrunoLiegiBastonLiegi 's comment to move some clifford_utils functions to the CliffordBackend.