OpenQudit: Extensible and Accelerated Numerical Quantum Compilation via a JIT-Compiled DSL

High-performance numerical quantum compilers rely on classical optimization, but are limited by slow numerical evaluations and a design that makes extending them with new instructions a difficult, error-prone task for domain experts. This talk starts by introducing numerical quantum compilation with state-of-the-art tools. Then it introduces OpenQudit, a compilation framework that solves these problems by allowing users to define quantum operations symbolically in the Qudit Gate Language (QGL), a mathematically natural DSL. OpenQudit's ahead-of-time compiler uses a tensor network representation and an e-graph-based pass for symbolic simplification before a runtime tensor network virtual machine (TNVM) JIT-compiles the expressions into high-performance native code. The evaluation shows that this symbolic approach is highly effective, accelerating core numerical tasks by up to 20 times on common quantum circuit synthesis problems compared to state-of-the-art tools.