BDD2Seq: Enabling Scalable Reversible-Circuit Synthesis via Graph-to-Sequence Learning

2025-11-11

AI Summary

Optimizing variable ordering for binary decision diagrams (BDDs) in reversible circuit synthesis is an NP-complete problem; existing heuristics suffer substantial performance degradation as circuit size increases. This paper proposes the first end-to-end graph-to-sequence learning framework: it models the circuit netlist as a heterogeneous graph, employs a graph neural network (GNN) encoder to capture structural dependencies, and utilizes a pointer network decoder to generate variable orders, augmented by a diversity-aware beam search to enhance solution quality. To our knowledge, this is the first work integrating GNNs with pointer networks for BDD variable ordering. Evaluated on three public benchmarks, our method achieves an average 1.4× reduction in quantum cost and a 3.7× speedup in synthesis time over state-of-the-art approaches. The framework demonstrates high efficiency, strong scalability, and superior generalization across diverse circuit families.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Binary Decision Diagrams (BDDs) are instrumental in many electronic design automation (EDA) tasks thanks to their compact representation of Boolean functions. In BDD-based reversible-circuit synthesis, which is critical for quantum computing, the chosen variable ordering governs the number of BDD nodes and thus the key metrics of resource consumption, such as Quantum Cost. Because finding an optimal variable ordering for BDDs is an NP-complete problem, existing heuristics often degrade as circuit complexity grows. We introduce BDD2Seq, a graph-to-sequence framework that couples a Graph Neural Network encoder with a Pointer-Network decoder and Diverse Beam Search to predict high-quality orderings. By treating the circuit netlist as a graph, BDD2Seq learns structural dependencies that conventional heuristics overlooked, yielding smaller BDDs and faster synthesis. Extensive experiments on three public benchmarks show that BDD2Seq achieves around 1.4 times lower Quantum Cost and 3.7 times faster synthesis than modern heuristic algorithms. To the best of our knowledge, this is the first work to tackle the variable-ordering problem in BDD-based reversible-circuit synthesis with a graph-based generative model and diversity-promoting decoding.

Problem

• Optimizing variable ordering in BDD-based reversible-circuit synthesis
• Reducing Quantum Cost and synthesis time for scalable quantum computing
• Learning structural dependencies in circuit netlists using graph-to-sequence models

Innovation

• Uses Graph Neural Network encoder for structural dependencies
• Employs Pointer-Network decoder with Diverse Beam Search
• Treats circuit netlist as graph for ordering prediction