Drop support for Python 3.7 (Qiskit#10009)

* Drop support for Python 3.7

This updates our documentation and build processes to set Python 3.8 as
the oldest support version of Python, consistent with our policy on
Python support.

This commit also removes remaining Python-version gating, since we were
principally using this to account for differences between 3.7 and 3.8.
Several backport packages are no longer required for any suppported
Python version, because of this change.

* Remove test for multiprocessing on Mac

With Python 3.7 support now dropped, there are no versions of Python on
macOS that we expect to support with multiprocessing again.  There's no
guarantee that the hypothetical Python 10.11 (???) that this test was
previously checking would be any more valid than existing versions.

---------

Co-authored-by: Matthew Treinish <[email protected]>

qiskit/algorithms/gradients/finite_diff_estimator_gradient.py

@@ -14,8 +14,8 @@
 
 from __future__ import annotations
 
-import sys
 from collections.abc import Sequence
+from typing import Literal
 
 import numpy as np
 
@@ -30,11 +30,6 @@
 
 from ..exceptions import AlgorithmError
 
-if sys.version_info >= (3, 8):
-    from typing import Literal
-else:
-    from typing_extensions import Literal
-
 
 class FiniteDiffEstimatorGradient(BaseEstimatorGradient):
     """

qiskit/algorithms/gradients/finite_diff_sampler_gradient.py

@@ -14,8 +14,8 @@
 
 from __future__ import annotations
 
-import sys
 from collections import defaultdict
+from typing import Literal, Sequence
 
 import numpy as np
 
@@ -28,12 +28,6 @@
 
 from ..exceptions import AlgorithmError
 
-if sys.version_info >= (3, 8):
-    # pylint: disable=ungrouped-imports
-    from typing import Literal, Sequence
-else:
-    from typing_extensions import Literal
-
 
 class FiniteDiffSamplerGradient(BaseSamplerGradient):
     """

qiskit/algorithms/optimizers/optimizer.py

@@ -18,20 +18,13 @@
 from collections.abc import Callable
 from enum import IntEnum
 import logging
-import sys
-from typing import Any, Union
+from typing import Any, Union, Protocol
 
 import numpy as np
 import scipy
 
 from qiskit.algorithms.algorithm_result import AlgorithmResult
 
-if sys.version_info >= (3, 8):
-    # pylint: disable=ungrouped-imports
-    from typing import Protocol
-else:
-    from typing_extensions import Protocol
-
 logger = logging.getLogger(__name__)
 
 POINT = Union[float, np.ndarray]

qiskit/algorithms/optimizers/p_bfgs.py

@@ -16,7 +16,6 @@
 import logging
 import multiprocessing
 import platform
-import sys
 from collections.abc import Callable
 from typing import SupportsFloat
 
@@ -109,12 +108,11 @@ def minimize(
             # default. The fork start method should be considered unsafe as it can
             # lead to crashes.
             # However P_BFGS doesn't support spawn, so we revert to single process.
-            if sys.version_info >= (3, 8):
-                num_procs = 0
-                logger.warning(
-                    "For MacOS, python >= 3.8, using only current process. "
-                    "Multiple core use not supported."
-                )
+            num_procs = 0
+            logger.warning(
+                "For MacOS, python >= 3.8, using only current process. "
+                "Multiple core use not supported."
+            )
         elif platform.system() == "Windows":
             num_procs = 0
             logger.warning(