Remove examples/ directory (#13218)

* Remove examples/ directory

This commit removes the examples/ directory from Qiskit. At one time in
the past these scripts and qasm files served as a useful example for how
to get started with Qiskit. However the patterns shown in these examples
aren't very relevant anymore and have been superseded by the official
documentation and the numerous tutorials out there now. While these
examples still work as we've been running tests to validate they're
still functional on every commit, there is little value in keeping them
around. This commit removes the examples directory and all the files
contained within. The test_examples unittest module is also removed
since there is nothing left to test anymore.

* Remove other examples usage in Makefile and CONTRIBUTING.md

CONTRIBUTING.md

@@ -440,21 +440,21 @@ you can do this faster with the `-n`/`--no-discover` option. For example:
 
 to run a module:
 ```
-tox -epy310 -- -n test.python.test_examples
+tox -epy310 -- -n test.python.compiler.test_transpiler
 ```
 or to run the same module by path:
 
 ```
-tox -epy310 -- -n test/python/test_examples.py
+tox -epy310 -- -n test/python/compiler/test_transpiler.py
 ```
 to run a class:
 
 ```
-tox -epy310 -- -n test.python.test_examples.TestPythonExamples
+tox -epy310 -- -n test.python.compiler.test_transpiler.TestTranspile
 ```
 to run a method:
 ```
-tox -epy310 -- -n test.python.test_examples.TestPythonExamples.test_all_examples
+tox -epy310 -- -n test.python.compiler.test_transpiler.TestTranspile.test_transpile_non_adjacent_layout
 ```
 
 Alternatively there is a makefile provided to run tests, however this

Makefile

@@ -28,27 +28,25 @@ env:
 # Ignoring generated ones with .py extension.
 lint:
 	pylint -rn qiskit test tools
-	tools/verify_headers.py qiskit test tools examples
-	pylint -rn --disable='invalid-name, missing-module-docstring, redefined-outer-name' examples/python/*.py
+	tools/verify_headers.py qiskit test tools
 	tools/find_optional_imports.py
 	tools/find_stray_release_notes.py
 
 # Only pylint on files that have changed from origin/main. Also parallelize (disables cyclic-import check)
 lint-incr:
 	-git fetch -q https://github.com/Qiskit/qiskit-terra.git :lint_incr_latest
 	tools/pylint_incr.py -j4 -rn -sn --paths :/qiskit/*.py :/test/*.py :/tools/*.py
-	tools/pylint_incr.py -j4 -rn -sn --disable='invalid-name, missing-module-docstring, redefined-outer-name' --paths ':(glob,top)examples/python/*.py'
-	tools/verify_headers.py qiskit test tools examples
+	tools/verify_headers.py qiskit test tools
 	tools/find_optional_imports.py
 
 ruff:
-	ruff qiskit test tools examples setup.py
+	ruff qiskit test tools setup.py
 
 style:
-	black --check qiskit test tools examples setup.py
+	black --check qiskit test tools setup.py
 
 black:
-	black qiskit test tools examples setup.py
+	black qiskit test tools setup.py
 
 # Use the -s (starting directory) flag for "unittest discover" is necessary,
 # otherwise the QuantumCircuit header will be modified during the discovery.