Since for certain realizations of quantum circuits only adjacent qubits may interact, qubits have to be frequently swapped - leading to a significant overhead. Therefore, optimizations such as exact global reordering have been proposed, where qubits are reordered such that the overall number of swaps is minimal. However, to guarantee minimality all n! possible permutations of qubits have to be considered in the worst case - which becomes intractable for larger circuits. In this work, we tackle the complexity of exact global reordering using an A~* search algorithm. The sophisticated heuristics for the search algorithm proposed in this paper allow for solving the problem in a much more scalable fashion. In fact, experimental evaluations show that the proposed approach is capable of determining the best order of the qubits for circuits with up to 25 qubits, whereas the recent state-of-the-art already reaches its limits with circuits composed of 10 qubits.
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