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

2026-05-12

AI Summary

This work addresses the NP-hard problem of dynamic qubit routing in quantum compilation by formulating it for the first time as a dynamic Quadratic Assignment Problem (QAP), where the logical gate interactions define the flow matrix and the hardware topology defines the distance matrix, yielding a unified optimization objective. The authors propose a Solution-aware Transformer policy network that explicitly captures interactions between the flow and distance matrices, augmented with a look-ahead mechanism naturally aligned with the QAP structure, enabling global routing decisions through reinforcement learning. Evaluated on three benchmarks—MQTBench, AgentQ, and QUEKO—the approach reduces CNOT gate counts by 15.7%, 30.4%, and 12.1%, respectively, significantly outperforming existing industrial 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.

Problem

• qubit routing
• quantum compilation
• Quadratic Assignment Problem
• NP-hard
• quantum circuits

Innovation

• Quadratic Assignment Problem
• Qubit Routing
• Reinforcement Learning
• Transformer Architecture
• Quantum Compilation