multiple tutorials broken when using real hardware

[natestemen]

Many of the tutorials are run on simulators, but have a variable that allow the reader to change the execution path to a quantum device. E.g. variable USE_REAL_HARDWARE in https://mitiq.readthedocs.io/en/stable/examples/ibmq-backends.html
This path is not tested by our documentation and is likely broken for multiple examples since IBM has started deprecating some functionality.

First thing we need to do is figure out which examples are broken so we can fix them.

[bdg221]

This is actually a bit more complicated than initially anticipated. With the removal of backend.run(), the new proposed method uses qiskit_ibm_runtime. Specifically, it uses SamplerV2 or EstimatorV2 from qiskit_ibm_runtime. Currently, the requirements/requirements-qiskit.txt has qiskit-ibm-runtime~=0.20.0. Unfortunately, 0.20.0 does not include SamplerV2 or EstimatorV2 primatives. The earliest version that includes those primatives is 0.21.1 and the latest version if 0.35.0.

I have found some dependency conflicts and I am doing more testing to determine the specific versions of packages that will be required to be able to run the tutorials on IBM's hardware.