Routing using graph partitioning (#117)

* introduce compiliation settings

* add compilation settings tests

* implement graph partitioning initial placement

* implement graph partitioning routing

* extract greedy routing alg

* add grid arch + tests

* add debug printing, grid test

* add routing example notebook

* Make mt-kahypar optional, skip tests that require mtkahypar

* Add Ion Shuttling section in readme

* Add more documentation

* more docstrings

* fix mypy errors and add some more docstrings

* update changelog

* update changelog

* fix shuttle penalty function

* some more small fixes

* document custom gates

* remove unnecessary comments + TODO

* add copyright where missing

* review suggestions

Author: trvto

README.md

@@ -31,6 +31,10 @@ prompt will store it in memory for further API use. Skip the prompt to see the a
 simulators. It is also possible to store and use your access token across sessions using
 `config.set_aqt_config`.
 
+## Ion Shuttling
+
+The `AQTMultiZoneBackend` supports routing of a circuit to a particular segmented ion-trap architecture before submission. This feature is experimental and not necessary for any currently available AQT devices. In order to use the graph partitioning based algorithms within this context, a manual installation of the [mt-kahypar](https://github.com/kahypar/mt-kahypar) package is necessary. See the instructions there for details.
+
 ## Bugs, support and feature requests
 
 Please file bugs and feature requests on the Github

docs/changelog.rst

@@ -1,6 +1,11 @@
 Changelog
 ~~~~~~~~~
 
+Unreleased
+----------
+
+* Add graph partition based routing for AQTMultiZoneBackend
+
 0.34.0 (August 2024)
 --------------------