Default set to turn off approximation_degree

[nonhermitian]

Summary

approximation_degree breaks unitary equivalence of the transpiler. This sets the default to off unless explicitly set.

Details and comments

A related issue (which I have not modified here) is that both approximation_degree=1.0 and approximation_degree=0 turn off the feature due to a bug (per the documentation 1.0 turns it off). However when thinking about "degree(s)" in other contexts, lower usually means less. And therefore 1.0 should actually be maximum approximation rather than none. This also aligns with boolean values. I think the code should be changed to reflect this.

[mtreinish]

I'm in favor of doing this because I agree this is a bad default. However, before we can merge this it needs a release note. Since this is an API change and users are potentially relying on the previous default (pretty much anyone running QV on hardware for real cares about this) the key thing for this PR is to have a release note that documents the change and provides a thorough explanation of why we're breaking things and how users can update if they desire the old default behavior. The process for adding release notes is here: https://github.com/Qiskit/qiskit-terra/blob/main/CONTRIBUTING.md#release-notes

[nonhermitian]

Yes. However I did not want to write a note until the second point about definition of what degree means is resolved. I am happy to make that change here as well.

[kdk]

Yes. However I did not want to write a note until the second point about definition of what degree means is resolved. I am happy to make that change here as well.

I think saying something like "approximation_degree is being disabled" should be sufficient. (For what it's worth, approximation_degree is defined, albeit loosely, here

https://github.com/Qiskit/qiskit-terra/blob/367ed4e34a3d662ef8ed8f2b91e8823bba1b8ca8/qiskit/compiler/transpiler.py#L178

There's a bug in handling approximation_degree IIRC in the TwoQubitBasisComposer (by this point, basis_fidelity)

https://github.com/Qiskit/qiskit-terra/blob/dbc81a8dcdae9e9294b9058babf5883258daaa5d/qiskit/quantum_info/synthesis/two_qubit_decompose.py#L1087

that causes the transpiler to erroneously treat approximation_degree=0.0 as approximation_degree=None).

[nonhermitian]

Is there one kind of release note preferred over others here? I am thinking "other" but open to whatever type people want.

[jakelishman]

We use "upgrade" (the section heading is called "API changes" in the built notes) to describe things users should be aware of in the new version - that could be a choice?

[nonhermitian]

Ok, will change to "upgrade"

[mtreinish]

This LGTM thanks for adding the release note. I just have some inline suggestions to make some small tweaks to the release note, then I think this should be good to go.