Exact and Practical Pattern Matching for Quantum Circuit Optimization

Quantum computations are typically performed as a sequence of basic operations, called quantum gates. Different gate sequences, circuits, can implement the same overall computation. Since every additional takes time and introduces noise into system, it is important to find smallest possible circuit that implements given computation, especially for near-term devices execute only limited number gates before renders computation useless. An building block many optimization techniques pattern matching: large small circuit, we would like all maximal matches , in considering pairwise commutation In this work, present first classical algorithm matching provably finds efficient enough be practical sizes typical devices. We demonstrate numerically 1 combining our with known pattern-matching-based reduces count random by ∼ 30% further improve practically relevant circuits were already optimized state-of-the-art techniques.