Near-optimal circuit mapping with reduced search paths on IBM quantum architectures

Abstract

Due to technological constraints in the quantum devices, two-qubit gates can be executed only if their qubits are physically connected (neighbours). If all the qubits of the two-qubit gates in a circuit cannot be kept adjacent to each other, then a remapping has to be performed. We insert swap gates between two adjacent qubits to update the mapping of qubits, increasing the number of basic operations. Generally, the mapping problem was addressed in terms of two sub-problems in the related works, the global ordering by initial mapping and the re-ordering of qubits (local ordering). We propose a technique where these two sub-problems are combined together; the need of local ordering is greatly reduced. We divide the circuit into blocks such that every block contains maximum gates and all the interacting qubits within the blocks are connected. Swap operations are performed between two consecutive blocks, and a series of swap operations form a path. The shortest route between two successive blocks is acquired using a breadth first search strategy. The main objective is to provide a near-optimal solution in reduced time. Experiments were conducted using the latest versions of the 5-qubit IBM Q devices, and the effects of qubit connectivities on the circuit cost was also investigated.