Remove factorizers and linear solvers from algorithms (Qiskit#9832)

* Remove factorizers and linear solvers

* Add reno

* Remove shor from backend tests

* Fix reno

* Apply suggestions from code review

Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com>

* Apply review reno

---------

Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com>

qiskit/algorithms/__init__.py

@@ -179,19 +179,6 @@
    time_evolvers.trotterization
 
 
-Factorizers
------------
-
-Algorithms to find factors of a number.
-
-.. autosummary::
-   :toctree: ../stubs/
-   :nosignatures:
-
-   Shor
-   ShorResult
-
-
 Gradients
 ----------
 
@@ -203,18 +190,6 @@
    gradients
 
 
-Linear Solvers
---------------
-
-Algorithms to solve linear systems of equations.
-
-.. autosummary::
-   :toctree: ../stubs/
-   :nosignatures:
-
-   linear_solvers
-
-
 Minimum Eigensolvers
 ---------------------
 
@@ -343,8 +318,6 @@
     EstimationProblem,
 )
 from .eigen_solvers import NumPyEigensolver, Eigensolver, EigensolverResult, VQD, VQDResult
-from .factorizers import Shor, ShorResult
-from .linear_solvers import HHL, LinearSolver, NumPyLinearSolver, LinearSolverResult
 from .minimum_eigen_solvers import (
     VQE,
     VQEResult,
@@ -411,17 +384,11 @@
     "EvolutionProblem",
     "TimeEvolutionResult",
     "TimeEvolutionProblem",
-    "LinearSolverResult",
     "Eigensolver",
     "EigensolverResult",
-    "Shor",
-    "ShorResult",
     "VQE",
     "VQEResult",
     "QAOA",
-    "LinearSolver",
-    "HHL",
-    "NumPyLinearSolver",
     "NumPyMinimumEigensolver",
     "MinimumEigensolver",
     "MinimumEigensolverResult",