Title: Scalable Pattern Matching in Computation Graphs

Abstract: Graph rewriting is a popular tool for the optimisation and modification of graph expressions in domains such as compilers, machine learning and quantum computing. The underlying data structures are often port graphs - graphs with labels at edge endpoints. These port labels greatly simplify pattern matching.
A pre-requisite for graph rewriting is the ability to find subgraphs of the input that match known graph identities: the pattern matching problem. We propose a new solution to pattern matching in port graphs. Its novelty lies in the use of a pre-computed data structure that makes the pattern matching runtime complexity independent of the number of patterns. The runtime is bound by the maximum width $w$ and depth $d$ of the patterns, as well as the input graph size $|G|$ as $O(|G| \cdot c^w / w^{1/2} \cdot d)$ with $c = 6.75$. This offers a significant advantage over existing solutions for use cases where patterns have low width and the set of patterns is large and fixed ahead of time.
In the context of quantum circuits, pattern width can be limited to qubit number. Quantum superoptimisers may use thousands of rewrite rules on circuits with less than 5 qubits, making them an ideal use case. We provide benchmarks showing that our algorithm offers a 20x speedup over current implementations on a dataset of 10'000 real world patterns describing quantum circuits.