Optimized Quantum Circuit Generation with SPIRAL

Quantum computers have been at the bleeding edge of computing technology for nearly 40 years and promise to make several classically-difficult problems tractable. However, despite many hardware and algorithm breakthroughs, the software infrastructure that compiles programs for these devices requires further development in order to produce sufficiently scalable code. In this work we present a novel approach to compiling more efficient quantum programs. Rather than mapping individual programs onto quantum hardware, we capture the input as a high-level mathematical transform and generate a multitude of architecture-compliant programs directly from that specification, allowing us to search over a much larger space of implementations to select the best output. Specifically, this is achieved by casting circuit generation as a sparse matrix factorization task and recursively searching over a host of divide-and-conquer decomposition rules. By generating programs from the top-down, we retain high-level information about the program we are compiling and can explore algorithm-specific rewrites that are nearly impossible to recognize given only a program stream. We implement the proposed framework [33] [34] with SPIRAL [18], a code generation platform founded on the GAP [42] computer algebra system; we ultimately demonstrate that SPIRAL is a promising supplemental tool for future quantum frameworks.