Classical Compiler Passes, Quantum Edition: Static Analyses for Quantum Programs

The remarkable sophistication of modern classical compilers suggests a blueprint for quantum software engineering: many optimizations are instances of a small number of semantic analysis patterns such as constant propagation, partial-redundancy elimination, side-effect or I/O optimization, and liveness-based dead-code elimination. In this manuscript, we show how these patterns can be transferred to quantum programs by endowing them with appropriate quantum semantics. Using several of our previously developed analyses as case studies, we demonstrate how classical passes admit quantum versions that effectively simplify quantum programs while preserving their semantics. Viewing quantum compilers through this lens provides a route towards robust optimization pipelines in quantum software stacks.