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Implement IBM's CXX compiler
Following Qiskit Terra's recently merged code, I found PR 6551 which purports to implement "optimal decomposition" of PU(4) into a sequence of "CAN(alpha, 0, 0)" (for varying alpha) based off of "internal, nearly-published theory work." (Quote marks are to indicate actual quotations from the PR.) Poking through the PR, it seems to use some of the conceptual tooling from the monodromy polytope paper. (Whenever the publication is out, I suppose we will see.)
The PR is pretty hefty, has lots of algebra and geometry, but nothing too extraordinarily daunting. It may be worth it to implement this functionality in quilc. Quilc has most of the scaffolding already to implement the compiler without fuss, so most of the trouble would be understanding and implementing the mathematics faithfully.
Paper about the technique got published.