QAP-Router: Tackling Qubit Routing as Dynamic Quadratic Assignment with Reinforcement Learning

TL;DR

QAP-Router introduces a reinforcement learning approach using a dynamic Quadratic Assignment Problem formulation and a Transformer-based policy network to improve qubit routing efficiency in quantum compilation.

Contribution

It models qubit routing as a dynamic QAP and employs a solution-aware Transformer with lookahead, capturing structure for better routing decisions.

Findings

Reduces CNOT gate count by 15.7% on MQTBench circuits.

Achieves 30.4% reduction on AgentQ datasets.

Improves routing efficiency over existing industry compilers.

Abstract

Qubit routing is a fundamental problem in quantum compilation, known to be NP-hard. Its dynamic nature makes local routing decisions propagate and compound over time, making global efficient solutions challenging. Existing heuristic methods rely on local rules with limited lookahead, while recent learning-based approaches often treat routing as a generic sequential decision problem without fully exploiting its underlying structure. In this paper, we introduce QAP-Router, framing qubit routing based on a dynamic Quadratic Assignment Problem (QAP) formulation. By modeling logical interactions, or quantum gates, as flow matrices and hardware topology as a distance matrix, our approach captures the interaction-distance coupling in a unified objective, which defines the reward in the reinforcement learning environment. To further exploit this structure, the policy network employs a solution-aware Transformer backbone that encodes the interaction between the flow matrix and the distance matrix into the attention mechanism. We also integrate a lookahead mechanism that blends naturally into the QAP framework, preventing myopic decisions. Extensive experiments on 1,831 real-world quantum circuits from the MQTBench, AgentQ and QUEKO datasets show that our method substantially reduces the CNOT gate count of routed circuits by 15.7%, 30.4% and 12.1%, respectively, relative to existing industry compilers.