Fix qpy for multiple controlled parametrized gates

[ElePT]

Summary

I have recently found out that if a circuit contains multiple instances of parametrized controlled gates of the same class
(not custom, for example, multiple ccrx, ccry....), the parameter values from the first instance were used to build the gate definitions of subsequent instances. This happened because they were all detected as the same custom_operation because of the shared gate class name.

The "fast" way I have found to address the issue has been to modify _write_instruction to account for the uuids of all controlled gates, to make sure they are not lumped into the same definition even if their parameter values are different. This is, however, not ideal because we might (will) be unnecessarily storing identical controlled gate definitions.

Given that the parameter values are actually correctly stored in the controlled gate payload (they are just never used because the definition is already bound to the values of the first gate), I think that an alternative could be to store an "unbound" version of the operation definition during write, and then assign the right parameter values to every instance during read, or keep it as-is and replace the incorrect values with the correct values. However, it looked a bit artificial and couldn't come up with a nice implementation.

Details and comments

Fixes #10735. Let me know if you think I should reconsider the implementation, as you can see, I am not too sure.

[qiskit-bot]

One or more of the the following people are requested to review this:

• @Qiskit/terra-core
• @mtreinish
• @nkanazawa1989

[jakelishman]

Sorry for the delay - this looks good to me, thanks. I was worried at first that it would cause us to write out different descriptions of all our standard controlled gate (like cx), but that's not true because it only affects gates that are exact instances of ControlledGate.