Switch tests and documentation to use qiskit-ibm-runtime fake backends

The IBM-specific fake backends in Qiskit are being removed in Qiskit 1.0
in Qiskit/qiskit#11376. The same fake backends
have been moved to qiskit-ibm-runtime in
Qiskit/qiskit-ibm-runtime#1140 and follow up
PRs.

Here the `qiskit` imports are replaced with `qiskit-ibm-runtime` imports
in order to provide a smooth transition between Qiskit 0.45 and Qiskit
1.0. In the future, it may be preferable to use generic fake backends
maintained in the repo and not depend on `qiskit-ibm-runtime` for them.

Additionally, this commit reorders the requirements-dev.txt file so it
is easier to read and adds qiskit-ibm-runtime as a development
dependency.

docs/manuals/characterization/stark_experiment.rst

@@ -112,9 +112,13 @@ drive port of the qubit.
 In a typical IBM device using the cross-resonance drive architecture,
 such channel can be identified with your backend as follows:
 
+.. note::
+    This tutorial requires the :mod:`qiskit_ibm_runtime` package to model a
+    backend.  You can install it with ``python -m pip install qiskit-ibm-runtime``.
+
 .. jupyter-execute::
 
-    from qiskit.providers.fake_provider import FakeHanoiV2
+    from qiskit_ibm_runtime.fake_provider import FakeHanoiV2
 
     backend = FakeHanoiV2()
     qubit = 0
@@ -143,7 +147,7 @@ by a variant of the Hahn-echo pulse sequence [5]_.
 
     from qiskit_experiments.library import StarkRamseyXY
     from qiskit import schedule, pulse
-    from qiskit.providers.fake_provider import FakeHanoi
+    from qiskit_ibm_runtime.fake_provider import FakeHanoi
     from qiskit.visualization.pulse_v2 import IQXSimple
 
     backend = FakeHanoi()

docs/manuals/characterization/t1.rst

@@ -30,8 +30,9 @@ The following code demonstrates a basic run of a :math:`T_1` experiment
 for qubit 0.
 
 .. note::
-    This manual requires the :mod:`qiskit_aer` package to run simulations.
-    You can install it with ``python -m pip install qiskit-aer``.
+    This tutorial requires the :mod:`qiskit_aer` and :mod:`qiskit_ibm_runtime`
+    packages to run simulations.  You can install them with ``python -m pip
+    install qiskit-aer qiskit-ibm-runtime``.
 
 .. jupyter-execute::
 
@@ -42,9 +43,9 @@ for qubit 0.
     from qiskit_experiments.library.characterization.analysis.t1_analysis import T1KerneledAnalysis
 
     # A T1 simulator
-    from qiskit.providers.fake_provider import FakePerth
     from qiskit_aer import AerSimulator
     from qiskit_aer.noise import NoiseModel
+    from qiskit_ibm_runtime.fake_provider import FakePerth
 
     # A kerneled data simulator
     from qiskit_experiments.test.mock_iq_backend import MockIQBackend

docs/manuals/characterization/t2ramsey.rst

@@ -58,13 +58,14 @@ We run the experiment on a simulated backend using Qiskit Aer with a
 pure T1/T2 relaxation noise model.
 
 .. note::
-    This manual requires the :mod:`qiskit_aer` package to run simulations.
-    You can install it with ``python -m pip install qiskit-aer``.
+    This tutorial requires the :mod:`qiskit_aer` and :mod:`qiskit_ibm_runtime`
+    packages to run simulations.  You can install them with ``python -m pip
+    install qiskit-aer qiskit-ibm-runtime``.
 
 .. jupyter-execute::
 
     # A T1 simulator
-    from qiskit.providers.fake_provider import FakePerth
+    from qiskit_ibm_runtime.fake_provider import FakePerth
     from qiskit_aer import AerSimulator
     from qiskit_aer.noise import NoiseModel
 

docs/manuals/characterization/tphi.rst

@@ -21,8 +21,9 @@ From the :math:`T_1` and :math:`T_2` estimates, we compute the results for
 :math:`T_\varphi.`
 
 .. note::
-    This manual requires the :mod:`qiskit_aer` package to run simulations.
-    You can install it with ``python -m pip install qiskit-aer``.
+    This tutorial requires the :mod:`qiskit_aer` and :mod:`qiskit_ibm_runtime`
+    packages to run simulations.  You can install them with ``python -m pip
+    install qiskit-aer qiskit-ibm-runtime``.
 
 .. jupyter-execute::
 
@@ -31,9 +32,9 @@ From the :math:`T_1` and :math:`T_2` estimates, we compute the results for
     from qiskit_experiments.library.characterization import Tphi
 
     # An Aer simulator
-    from qiskit.providers.fake_provider import FakePerth
     from qiskit_aer import AerSimulator
     from qiskit_aer.noise import NoiseModel
+    from qiskit_ibm_runtime.fake_provider import FakePerth
 
     # Create a pure relaxation noise model for AerSimulator
     noise_model = NoiseModel.from_backend(

docs/manuals/measurement/readout_mitigation.rst

@@ -31,8 +31,9 @@ This notebook demonstrates the usage of both the local and correlated
 experiments to generate the corresponding mitigators.
 
 .. note::
-    This manual requires the :mod:`qiskit_aer` package to run simulations.
-    You can install it with ``python -m pip install qiskit-aer``.
+    This tutorial requires the :mod:`qiskit_aer` and :mod:`qiskit_ibm_runtime`
+    packages to run simulations.  You can install them with ``python -m pip
+    install qiskit-aer qiskit-ibm-runtime``.
 
 .. jupyter-execute::
 
@@ -43,7 +44,7 @@ experiments to generate the corresponding mitigators.
     from qiskit_experiments.library import LocalReadoutError, CorrelatedReadoutError
 
     from qiskit_aer import AerSimulator
-    from qiskit.providers.fake_provider import FakePerth
+    from qiskit_ibm_runtime.fake_provider import FakePerth
 
     from qiskit.result.mitigation.utils import (
         expval_with_stddev,