Optimizing Quantum Circuits, Fast and Slow

Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this work we unify two disparate ideas for optimizing quantum circuits, rewrite rules, which are fast standard optimizer passes, and unitary synthesis, which is slow, requiring a search through the space of circuits. We present a clean, unifying framework for thinking of rewriting and resynthesis as abstract circuit transformations. We then present a radically simple algorithm, GUOQ, for optimizing quantum circuits that exploits the synergies of rewriting and resynthesis. Our extensive evaluation demonstrates the ability of GUOQ to strongly outperform existing optimizers on a wide range of benchmarks and gate sets. For instance, GUOQ outperforms state-of-the-art optimizers on at least 80% of the benchmark suite with respect to two-qubit gate reduction on the IBM gate sets. In particular, GUOQ achieves an average of 28% two-qubit gate reduction on the IBM Eagle gate set while the state-of-the-art superoptimizer, which requires a GPU, and industrial toolkit achieve average reductions of 18% and 7%, respectively.