Move linear_solvers package from qiskit-terra

qiskit_research/linear_solvers/__init__.py

@@ -0,0 +1,92 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2021, 2022.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""
+Linear solvers (:mod:`qiskit_research.linear_solvers`)
+=========================================================
+It  contains classical and quantum algorithms to solve systems of linear equations such as
+:class:`~qiskit_research.linear_solvers.HHL`.
+Although the quantum algorithm accepts a general Hermitian matrix as input, Qiskit's default
+Hamiltonian evolution is exponential in such cases and therefore the quantum linear solver will
+not achieve an exponential speedup.
+Furthermore, the quantum algorithm can find a solution exponentially faster in the size of the
+system than their classical counterparts (i.e. logarithmic complexity instead of polynomial),
+meaning that reading the full solution vector would kill such speedup (since this would take
+linear time in the size of the system).
+Therefore, to achieve an exponential speedup we can only compute functions from the solution
+vector (the so called observables) to learn information about the solution.
+Known efficient implementations of Hamiltonian evolutions or observables are contained in the
+following subfolders:
+
+`Matrices`_
+  A placeholder for efficient implementations of the Hamiltonian evolution of particular types of
+  matrices.
+
+`Observables`_
+  A placeholder for efficient implementations of functions that can be computed from the solution
+  vector to a system of linear equations.
+
+.. currentmodule:: qiskit_research.linear_solvers
+
+Linear Solvers
+==============
+
+.. autosummary::
+   :toctree: ../stubs/
+   :nosignatures:
+
+   LinearSolver
+   LinearSolverResult
+   HHL
+   NumPyLinearSolver
+
+Matrices
+========
+
+.. autosummary::
+   :toctree: ../stubs/
+   :nosignatures:
+
+   LinearSystemMatrix
+   NumPyMatrix
+   TridiagonalToeplitz
+
+Observables
+===========
+
+.. autosummary::
+    :toctree: ../stubs/
+
+    LinearSystemObservable
+    AbsoluteAverage
+    MatrixFunctional
+
+"""
+
+from .hhl import HHL
+from .numpy_linear_solver import NumPyLinearSolver
+from .linear_solver import LinearSolver, LinearSolverResult
+from .matrices import LinearSystemMatrix, NumPyMatrix, TridiagonalToeplitz
+from .observables import LinearSystemObservable, AbsoluteAverage, MatrixFunctional
+
+__all__ = [
+    "HHL",
+    "NumPyLinearSolver",
+    "LinearSolver",
+    "LinearSolverResult",
+    "LinearSystemMatrix",
+    "NumPyMatrix",
+    "TridiagonalToeplitz",
+    "LinearSystemObservable",
+    "AbsoluteAverage",
+    "MatrixFunctional",
+]