From Bit-Parallelism to Quantum String Matching for Labelled Graphs

• URL: http://arxiv.org/abs/2302.02848v2
• Date: Fri, 14 Apr 2023 12:40:39 GMT
• Title: From Bit-Parallelism to Quantum String Matching for Labelled Graphs
• Authors: Massimo Equi, Arianne Meijer - van de Griend, Veli M\"akinen
• Abstract summary: Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. We show that a simple bit-parallel algorithm on such restricted family of graphs can indeed be converted into a realistic quantum algorithm.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in $O(n^2/w)$ time. In a reasonable classical model of computation, one can assume $w=\Theta(\log n)$, and obtaining significantly better speed-ups is unlikely in the light of conditional lower bounds obtained for such problems. In this paper, we study the connection of bit-parallelism to quantum computation, aiming to see if a bit-parallel algorithm could be converted to a quantum algorithm with better than logarithmic speed-up. We focus on string matching in labeled graphs, the problem of finding an exact occurrence of a string as the label of a path in a graph. This problem admits a quadratic conditional lower bound under a very restricted class of graphs (Equi et al. ICALP 2019), stating that no algorithm in the classical model of computation can solve the problem in time $O(|P||E|^{1-\epsilon})$ or $O(|P|^{1-\epsilon}|E|)$. We show that a simple bit-parallel algorithm on such restricted family of graphs (level DAGs) can indeed be converted into a realistic quantum algorithm that attains subquadratic time complexity $O(|E|\sqrt{|P|})$.

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