A Dynamic Look-Ahead Heuristic for the Qubit Mapping Problem of NISQ Computers

In the past few years, several quantum computers realized by the noisy intermediate-scale quantum (NISQ) technology have been released. However, there exists a significant limitation to using such computers, i.e., the connectivity constraint between physical qubits. To perform a 2-qubit quantum operation on such NISQ computers, its two logical qubits have to be mapped to a pair of physical qubits that satisfy the connectivity constraint. This mapping procedure requires additional operations to be introduced into the original quantum circuit, reducing its fidelity. Therefore, it is of great significance to design an algorithm that is able to complete the mapping task with minimal additional operations. In this article, we propose an efficient algorithm to solve this problem. Our algorithm consists of two core components, an expansion-from-center scheme to determine the initial mapping and a SWAP-based heuristic search algorithm to update the mapping. We introduce the maximum consecutive positive effect of a SWAP operation as the heuristic cost function, allowing our search algorithm to look ahead dynamically. Our algorithm is evaluated on IBM Q 20. The experimental results show that our algorithm can complete the mapping task in a very short time even for large-scale benchmarks with hundreds of thousands of operations, and outperforms the state-of-the-art in terms of the number of additional operations for most benchmarks considered.