Combining SWAPs and Remote CNOT Gates for Quantum Circuit Transformation

Quantum computers offer enormous speed advantages over their classical counterparts. Still, optimization on quantum circuits is necessary to further increase their potential. Additionally, physical realizations of quantum computers place restrictions on quantum circuits, regarding the available quantum gates. In order to satisfy these restrictions, non-native gates need to be expressed as an equivalent cascade of natively available quantum gates which induces a mapping overhead. Two complementary approaches to this problem are to move around the qubits (using SWAP gates) or to apply so-called remote gates, i.e. pre-computed cascades of native gates which keep the qubit placement.In this paper, we explore how combinations of movements and remote gates can be employed to reduce the required overhead regarding the number of native gates as well as the circuit depth. We also discuss ways to find out which qubits to address with the movements in order to optimize these metrics. Our general evaluation is supplemented by evaluations on two IBM quantum computer architectures to show how quantum circuits can be optimized by the presented patterns.