Learned Intermediate Representations in Quantum Compilers

This preprint introduces a conceptual and experimental framework for integrating learned continuous representations into quantum compiler architectures. Modern quantum compilers rely on symbolic intermediate representations and rule-based transformation passes applied over circuit graphs. While effective, such approaches are inherently discrete and constrained by handcrafted rewrite rules and heuristic search strategies. This work proposes a Learned Intermediate Representation (LIR) paradigm in which quantum circuits are embedded into a continuous latent space. Within this framework: Circuit graphs are mapped to fixed-dimensional embeddings. Latent representations capture structural and operational properties of quantum circuits. Learned models guide symbolic transformation selection. Structural validity and physical correctness are enforced by a symbolic compilation layer. The proposed approach does not replace existing compilation infrastructures. Instead, it augments traditional symbolic pipelines with a learnable representation layer that enables data-driven optimization strategies while preserving correctness guarantees. The preprint includes: A formal definition of the encoder and latent representation space. A hybrid neural-symbolic decoding formulation. An experimental methodology for comparing neural-guided and rule-based compilation. Evaluation metrics focused on structural cost reduction (e.g., two-qubit gate count). Discussion of theoretical considerations, limitations, and future research directions. This work represents an initial investigation into continuous intermediate representations for quantum compilation and is intended as a foundation for further research in adaptive and data-driven compiler design.