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The recent progress in the physical realization of quantum computers (thefirst publicly available ones--IBM's QX architectures--have been launched in2017) has motivated research on automatic methods that aid users in runningquantum circuits on them. Here, certain physical constraints given by thearchitectures which restrict the allowed interactions of the involved qubitshave to be satisfied. Thus far, this has been addressed by inserting SWAP and Hoperations. However, it remains unknown whether existing methods add a minimumnumber of SWAP and H operations or, if not, how far they are away from thatminimum--an NP-complete problem. In this work, we address this by formulatingthe mapping task as a symbolic optimization problem that is solved usingreasoning engines like Boolean satisfiability solvers. By this, we do not onlyprovide a method that maps quantum circuits to IBM's QX architectures with aminimal number of SWAP and H operations, but also show by experimentalevaluation that the number of operations added by IBM's heuristic solutionexceeds the lower bound by more than 100% on average. An implementation of theproposed methodology is publicly available athttp://iic.jku.at/eda/research/ibm_qx_mapping.

Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations