Integrate QRAO into Qiskit Optimization (#487)

* add qrao files

* support primitives and remove opflow

* update qrao

* update qrao

* add expecation_values getter

* inherit OptimizationAlgorithm

* add unittests for encoding

* add unittests for optimizer

* add unittests for optimizer

Co-authored-by: Jim Garrison <garrison@ibm.com>
Co-authored-by: Bryce Fuller <Bryce.Fuller@ibm.com>
Co-authored-by: Jennifer Glick <Jennifer.R.Glick@ibm.com>
Co-authored-by: Caleb Johnson <calebj1524@outlook.com>
Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>
Co-authored-by: Toshinari Itoko <itoko@jp.ibm.com>
Co-authored-by: Areeq Hasan <areeq.i.hasan@gmail.com>

* add reno and unittests for magic rounding

* clean up

* remove a unnecessary file

* update the code

* add tutorial and update the code

* update pylintdict

* fix lint

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>

* Update qiskit_optimization/algorithms/qrao/magic_rounding.py

Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>

* Update releasenotes/notes/qrao-89d5ff1d2927de64.yaml

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

* update the code

* add explanations and reflect comments

* update codes

* fix

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

* update the code

* fix lint

* Fix docs so they build

* fix lint

* fix spell

* fix spell

* fix spell

* test

* test

* update

* fix lint

* use assertalmost equal in unittest

* update

* fix

* rerun tutorial

* add unittests for max per qubit= 2 and 1

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>

* fix docs

* lint

* add unittest quadratic objective

* update optimizer unittest

* replaces rustworkx with networkx

- updates type cast

* minor updates of explanation

* fix docstrings

* update an error message

* update error messages

* fix lint

* update tutorial and qiskit_algorithms

* update

* fix lint

* fix

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

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

* Update docs/tutorials/13_quantum_random_access_optimizer.ipynb

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

* fix

* Update qiskit_optimization/algorithms/qrao/__init__.py

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

* Update releasenotes/notes/qrao-89d5ff1d2927de64.yaml

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

* Update test/algorithms/qrao/test_magic_rounding.py

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

* Update test/algorithms/qrao/test_quantum_random_access_optimizer.py

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

* fix mypy

* fix

* fix

* change the index number

---------

Co-authored-by: Jim Garrison <garrison@ibm.com>
Co-authored-by: Bryce Fuller <Bryce.Fuller@ibm.com>
Co-authored-by: Jennifer Glick <Jennifer.R.Glick@ibm.com>
Co-authored-by: Caleb Johnson <calebj1524@outlook.com>
Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com>
Co-authored-by: Toshinari Itoko <itoko@jp.ibm.com>
Co-authored-by: Areeq Hasan <areeq.i.hasan@gmail.com>
Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com>
Co-authored-by: woodsp-ibm <woodsp@us.ibm.com>
Co-authored-by: Takashi Imamichi <imamichi@jp.ibm.com>

.pylintdict

@@ -10,6 +10,7 @@ apidocs
 applegate
 args
 arxiv
+atol
 autosummary
 backend
 backends
@@ -54,6 +55,7 @@ eigen
 eigensolver
 eigensolvers
 eigenstate
+embeddings
 entangler
 enum
 eq
@@ -83,6 +85,7 @@ hamilton
 hamiltonian
 hamiltonians
 hastings
+hayashi
 hoyer
 https
 ibm
@@ -111,6 +114,7 @@ lp
 lucas
 macos
 makefile
+masahito
 matplotlib
 maxcut
 maxfun
@@ -119,6 +123,8 @@ mdl
 milp
 minimizer
 minimumeigenoptimizer
+mmp
+mpm
 multiset
 mypy
 nannicini
@@ -133,6 +139,7 @@ np
 num
 numpy
 numpyminimumeigensolver
+observables
 october
 opflow
 optimality
@@ -146,8 +153,10 @@ parikh
 pauli
 paulis
 peleato
+pmm
 pooya
 pos
+ppp
 pre
 preprint
 prepend
@@ -163,6 +172,8 @@ qiskit
 qiskit's
 qn
 qp
+qrac
+qrao
 quadratically
 quadraticconstraint
 quadraticobjective
@@ -197,6 +208,7 @@ spsa
 src
 statevector
 stdout
+stephen
 str
 subcollection
 subgraph
@@ -232,6 +244,7 @@ xixj
 wavefunction
 wecker
 whitespace
+wiesner
 williamson
 xs
 ys

docs/apidocs/qiskit_optimization.algorithms.qrao.rst

@@ -0,0 +1,6 @@
+.. _qiskit_optimization-algorithms-qrao:
+
+.. automodule:: qiskit_optimization.algorithms.qrao
+   :no-members:
+   :no-inherited-members:
+   :no-special-members:

docs/explanations/index.rst

@@ -0,0 +1,23 @@
+################################
+Qiskit Optimization Explanations
+################################
+
+This section of the documentation provides background and explanation around techniques, methods
+etc. both useful with and used by in Qiskit Optimization.
+
+Explanations...
+---------------
+
+.. toctree::
+    :maxdepth: 1
+    :glob:
+
+    *
+
+|
+
+.. Hiding - Indices and tables
+   :ref:`genindex`
+   :ref:`modindex`
+   :ref:`search`
+