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The decomposition solver uses a generalized Dijkstra's algorithm - #3334
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…PennyLaneAI#10350) **Context:** We added `PPR_2/4/8` as frontend versions of Pauli product rotations and have quite a few decompositions using them already. The remaining translation of gates to PPRs currently is done in the Catalyst pass `to_ppr`. However, given that this is mere decomposition, we'd rather have it happen as part of `qp.decompose` to leverage graph solution quality. **Description of the Change:** Add most remaining decompositions that are part of `to_ppr` to the decomposition rule set. The only types of rule skipped for now are - the ones translating continuous-angle operations with static-valued angles to discrete PPR counterparts. This is not a task handled very well by the graph (because the resources differ very strongly depending on information that is not available at graph construction/solution time), so we leave this type of translation to well-designed discretization passes that leverage special angles into cheap gate sequences. - measurement translations (MidMeasure -> PPM). This is not needed because it is a simple lowering step, and it would lead to complications due to the interaction between measurement return values and the graph system. side note: as usual, touching decompositions led to some expected (doc)test outputs changing (tie-break is not stable against such changes). **Benefits:** More decomposition happens within `qp.decompose`. **Possible Drawbacks:** Some more (very short) cycles in the decomposition graph, but that's not really a problem because the solver needs to handle those anyways. It is noteworthy that we had some edge case of suboptimal solutions with the current solver, which will be remedied by PennyLaneAI/catalyst#3334. This is not blocking, though (did not find any regression in test suite, nor in a set of 20 cycle-constructing examples). **Related GitHub Issues:** Made with AI
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Co-authored-by: Ali Asadi <10773383+maliasadi@users.noreply.github.com>
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## main #3334 +/- ##
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+ Coverage 95.98% 96.21% +0.23%
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Context:
The current decomposition solver uses a DFS search, which is fast and efficient but fails to guarantee optimality, and struggles to handle cyclic decompositions without simply ignoring the rules involved in them.
Description of the Change:
The decomposition solver uses a generalization of Dijkstra's algorithm for hypergraphs.
Performance was measured with respect to the DFS implementation on graphs of up to 500 rules, 10s-100s of gate types, and is generally ~5-10% faster than the DFS implementation. The exception is on highly cyclic graphs, where the DFS solver incorrectly avoids rules previously labelled as cycles.
Benefits:
Guarantees an optimal solution and handles cyclic rules natively.
Possible Drawbacks:
Cannot handle negative/NaN weights in the graph.
Related GitHub Issues:
[sc-133667]
Primarily generated using LLMs. Reviewed and validated by @kipawaa