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

• URL: http://arxiv.org/abs/2605.12365v1
• Date: Tue, 12 May 2026 16:34:01 GMT
• Title: QAP-Router: Tackling Qubit Routing as Dynamic Quadratic Assignment with Reinforcement Learning
• Abstract summary: We introduce QAP-hard, framing qubit routing based on a dynamic Quadratic Assignment Problem (QAP) formulation.<n>Our approach captures the interaction-distance coupling in a unified objective, which defines the reward in the reinforcement learning environment.<n>We also integrate a lookahead mechanism that blends naturally into the QAP framework, preventing myopic decisions.
• Score: 4.928336013285668
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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