Qubit Mapping: The Adaptive Divide-and-Conquer Approach

TL;DR

This paper introduces ADAC, an adaptive divide-and-conquer algorithm for qubit mapping that significantly improves routing efficiency on NISQ devices by leveraging circuit partitioning and heuristics.

Contribution

The study presents a novel adaptive partitioning approach for qubit mapping that outperforms existing methods, especially on large and realistic quantum circuits.

Findings

ADAC improves routing efficiency by nearly 50% on IBM Tokyo architecture.

ADAC achieves around 18% improvement on grid-like architectures with larger qubit counts.

The approach effectively handles circuit partitioning and routing in near-term quantum hardware.

Abstract

The qubit mapping problem (QMP) focuses on the mapping and routing of qubits in quantum circuits so that the strict connectivity constraints imposed by near-term quantum hardware are satisfied. QMP is a pivotal task for quantum circuit compilation and its decision version is NP-complete. In this study, we present an effective approach called Adaptive Divided-And-Conqure (ADAC) to solve QMP. Our ADAC algorithm adaptively partitions circuits by leveraging subgraph isomorphism and ensuring coherence among subcircuits. Additionally, we employ a heuristic approach to optimise the routing algorithm during circuit partitioning. Through extensive experiments across various NISQ devices and circuit benchmarks, we demonstrate that the proposed ADAC algorithm outperforms the state-of-the-art method. Specifically, ADAC shows an improvement of nearly 50\% on the IBM Tokyo architecture. Furthermore, ADAC exhibits an improvement of around 18\% on pseudo-realistic circuits implemented on grid-like architectures with larger qubit numbers, where the pseudo-realistic circuits are constructed based on the characteristics of widely existing realistic circuits, aiming to investigate the applicability of ADAC. Our findings highlight the potential of ADAC in quantum circuit compilation and the deployment of practical applications on near-term quantum hardware platforms.