Combining SWAPs and Remote Toffoli Gates in the Mapping to IBM QX Architectures

Quantum computation received a steadily growing attention in recent years, especially supported by the emergence of publicly available quantum computers like the popular IBM QX series. In order to execute a reversible or quantum circuit on those devices, a mapping is required that replaces each reversible or quantum gate by an equivalent cascade of elementary, i.e. directly executable, gates-a task which tends to induce a significant mapping overhead. Several approaches have been proposed for this task which either rely on the swapping of physically adjacent qubits or the use of precomputed templates, so-called remote CNOT gates. In this paper, we show that combining both, swapping and remote gates, at the reversible circuit level has the prospect of significantly reducing the mapping overhead. We propose a methodology to compute the optimal combination of swaps and templates for Multiple-Controlled Toffoli gates. By using a formulation as a single-source shortest-path problem, a complete database of optimal combinations can be computed efficiently. Experimental results indicate that the mapping overhead can be significantly reduced.