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Optimal SWAP gate insertion for nearest neighbor quantum circuits

Motivated by its promising applications e.g. for database search or factorization, significant progress has been made in the development of automated design methods for quantum circuits. But in order to keep up with recent physical developments in this domain, new technological constraints have to be considered. Limited interaction distance between gate qubits is one of the most common of these constraints. This led to the development of several strategies aiming at making a given quantum circuit nearest neighbor-compliant by inserting SWAP gates into the existing structure. Usually these strategies are of heuristic nature. In this work, we present an exact approach that enables nearest neighbor-compliance by inserting a minimal number of SWAP gates. Experiments demonstrate the applicability of the approach which enabled a comparison of results obtained by heuristic methods to the actual optimum.