Enabling Dataflow Optimization for Quantum Programs

We propose an IR for quantum computing that directly exposes quantum and classical data dependencies for the purpose of optimization. Our IR consists of two dialects, one input dialect and one that is specifically tailored to enable quantum-classical co-optimization. While the first employs a perhaps more intuitive memory-semantics (quantum operations act as side-effects), the latter uses value-semantics (operations consume and produce states). Crucially, this encodes the dataflow directly in the IR, allowing for a host of optimizations that leverage dataflow analysis. We discuss how to map existing quantum programming languages to the input dialect and how to lower the resulting IR to the optimization dialect. We present a prototype implementation based on MLIR that includes several quantum-specific optimization passes. Our benchmarks show that significant improvements in resource requirements are possible even through static optimization. In contrast to circuit optimization at runtime, this is achieved while incurring only a small constant overhead in compilation time, making this a compelling approach for quantum program optimization at application scale.