Mapping a Quantum Circuit to 2D Nearest Neighbor Architecture by Changing the Gate Order

This paper proposes a new approach to optimize the number of necessary SWAP gates when we perform a quantum circuit on a two-dimensional (2D) NNA. Our new idea is to change the order of quantum gates (if possible) so that each sub-circuit has only gates performing on adjacent qubits. For each sub-circuit, we utilize a SAT solver to find the best qubit placement such that the sub-circuit has only gates on adjacent qubits. Each sub-circuit may have a different qubit placement such that we do not need SWAP gates for the sub-circuit. Thus, we insert SWAP gates between two sub-circuits to change the qubit placement which is desirable for the following sub-circuit. To reduce the number of such SWAP gates between two sub-circuits, we utilize A* algorithm.