🚧 MLIR | Implement QMAP Algorithm

[MatthiasReumann]

Description

This pull requests adds the MLIRized QMAP algorithm to the routing pass. A sub-goal of this pull request is to improve and simplify the existing implementation for performance and maintainability. The name of this "enhanced" QMAP algorithm isn't determined yet.

Noteworthy Changes

• Router: A router now is simply a (configurable) combination of a Layerizer and a Planner.
  • The layerizer decides which gates to route.
  • The planner searches / determines the sequence of SWAPs necessary to make the gates executable.
  • The router itself simply inserts SWAPs.
  • Moreover, the router is now also the primary driver of the pass. The RoutingContext has been removed and all member variables have been moved to the router implementation. This way, I think, we should be able to use this router also for layout-ing (To be shown).
• ThinLayout and Layout: The search nodes in the QMAP algorithm don't have to care about SSA values. Hence I added a new data structure, the ThinLayout, that simply maps program indices to hardware indices. The old Layout now inherits from this ThinLayout (Essentially a Layout is a fat ThinLayout). This way we can simply pass a Layout as ThinLayout and reduce the memory footprint of nodes.
• Pass Statistics: I've added a statistic nadd which counts the number of SWAPs added. Using statistics, we can also quite easily track the amount of milliseconds / seconds the routing took and print it via the -mlir-pass-statistics flag.

Algorithmic Changes:
Instead of computing all layers at startup, layers are computed on-demand. Moreover, the algorithm simply "steps over" already executable gates and doesn't include them in a layer (which to my knowledge the previous algorithm didn't). In other words, a layer always starts with a non-executable gate and crawls its way forward.

The (updated) cost function is

$$f\left(x\right) = \left(\alpha \cdot n_{swaps}\right) + \left(\beta \cdot n_{depth}\right) + \frac{1}{|gates|}\sum_{g \in gates}D[\pi(g.q1)][\pi (g.q2)] + \frac{\lambda}{|lookahead|}\sum_{g \in lookahead}D[\pi(g.q1)][\pi (g.q2)]$$

where $$n_{swaps}$$ is the number of swaps added, $$n_{depth}$$ is the additional "circuit" depth added by the swaps, and $$D$$ is the nearest neighbor length between $$g.q1$$ and $$g.q2$$.

$$\alpha, \beta, \gamma$$ are configurable variables.

Checklist:

• The pull request only contains commits that are focused and relevant to this change.
• I have added appropriate tests that cover the new/changed functionality.
• I have updated the documentation to reflect these changes.
• I have added entries to the changelog for any noteworthy additions, changes, fixes, or removals.
• I have added migration instructions to the upgrade guide (if needed).
• The changes follow the project's style guidelines and introduce no new warnings.
• The changes are fully tested and pass the CI checks.
• I have reviewed my own code changes.

[codecov]

Codecov Report

❌ Patch coverage is 96.56250% with 11 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...MQTOpt/Transforms/Transpilation/sc/RoutingPass.cpp	95.1%	5 Missing ⚠️
...ialect/MQTOpt/Transforms/Transpilation/Layerizer.h	94.1%	3 Missing ⚠️
.../Dialect/MQTOpt/Transforms/Transpilation/Planner.h	97.5%	2 Missing ⚠️
...t/MQTOpt/Transforms/Transpilation/Architecture.cpp	93.3%	1 Missing ⚠️

📢 Thoughts on this report? Let us know!