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[WIP] Use native bits and registers for CircuitData. #13686

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Summary

The following commits add native bits and register usage to CircuitData. This is the first public attempt at implementing these structures and is open to feedback.

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@raynelfss raynelfss linked an issue Jan 17, 2025 that may be closed by this pull request
raynelfss and others added 5 commits January 21, 2025 15:21
- Some functions in `CircuitData` had become mutable unnecessarily due to erroneous assumptions on the `BitData` `OnceCell` usage.
- Fix incorrect serialization to now include registers in `CircuitData::__reduce__`.
- Also add `CircuitData::__setstate__` to deal with the new register state.
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Make rust Qubit and Clbit the source of truth in a circuit
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