Recent accomplishments in the development of quantum circuits motivated research in Computer-Aided Design for quantum circuits. Here, how to consider physical constraints in general and so-called nearest neighbor constraints in particular is an objective of recent developments. Re-ordering the given qubits in a circuit provides thereby a common strategy in order to reduce the corresponding costs. But since this leads to a significant complexity, existing solutions either worked towards a single order only (and, hence, exclude better options) or suffer from high runtimes when considering all possible options. In this work, we provide an alternative which utilizes so-called πDDs for this purpose. They allow for the efficient representation and manipulation of sets of permutations and, hence, provide the ideal data-structure for the considered problem. Experimental evaluations confirm that, by utilizing πDDs, optimal or almost optimal results can be generated in a fraction of the time needed by exact solutions.
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