Deprecate the BIPMapping transpiler pass in favor of external plugin

This commit deprecates the BIPMapping transpiler pass. Since its
introduction the pass has been in a weird state since it's introduction.
It is a standalone transpiler pass that we never integrated it into
transpile() because it has an external dependency on cplex which is a
proprietary software package that most people don't have access too.
With the introduction of the transpiler stage plugin interface the pass
has been turned into an external package:

https://github.com/qiskit-community/qiskit-bip-mapper

By using the plugin interface the pass can now be cleanly integrates
into the transpile() function and also makes the requirement to have
cplex installed much more explicit. For users with cplex it's much
easier to run the BIPMapping pass as part of a transpilation workflow
with `transpile(..., routing_method="bip")`.

Closes #8662

qiskit/transpiler/passes/routing/algorithms/bip_model.py

@@ -26,6 +26,7 @@
     trace_to_fid,
 )
 from qiskit.utils import optionals as _optionals
+from qiskit.utils.deprecation import deprecate_func
 
 logger = logging.getLogger(__name__)
 
@@ -41,6 +42,12 @@ class BIPMappingModel:
             the solution will be stored in :attr:`solution`). None if it's not yet set.
     """
 
+    @deprecate_func(
+        since="0.24.0",
+        additional_msg="This has been replaced by a new transpiler plugin package: "
+        "qiskit-bip-mapper. More details can be found here: "
+        "https://github.com/qiskit-community/qiskit-bip-mapper",
+    )
     def __init__(self, dag, coupling_map, qubit_subset, dummy_timesteps=None):
         """
         Args:

qiskit/transpiler/passes/routing/bip_mapping.py

@@ -22,6 +22,7 @@
 from qiskit.transpiler import TransformationPass
 from qiskit.transpiler.exceptions import TranspilerError
 from qiskit.transpiler.passes.routing.algorithms.bip_model import BIPMappingModel
+from qiskit.utils.deprecation import deprecate_func
 
 logger = logging.getLogger(__name__)
 
@@ -62,6 +63,12 @@ class BIPMapping(TransformationPass):
     `arXiv:2106.06446 <https://arxiv.org/abs/2106.06446>`_
     """
 
+    @deprecate_func(
+        since="0.24.0",
+        additional_msg="This has been replaced by a new transpiler plugin package: "
+        "qiskit-bip-mapper. More details can be found here: "
+        "https://github.com/qiskit-community/qiskit-bip-mapper",
+    )
     def __init__(
         self,
         coupling_map,

releasenotes/notes/deprecate-bip-mapping-f0025c4c724e1ec8.yaml

@@ -0,0 +1,14 @@
+---
+deprecations:
+  - |
+    The transpiler routing pass, :class:`~.BIPMapping` has been deprecated
+    and will be removed in a future release. It has been replaced by an external
+    plugin package: ``qiskit-bip-mapper``. Details for this new package can
+    be found at the package's github repository:
+
+    https://github.com/qiskit-community/qiskit-bip-mapper
+
+    The pass was made into a separate plugin package for two reasons, first
+    the dependency on CPLEX makes it harder to use and secondly the plugin
+    packge more cleanly integrates with :func:`~.transpile`.
+