eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-06-21
9:1
9:20
10.4230/LIPIcs.CPM.2023.9
article
From Bit-Parallelism to Quantum String Matching for Labelled Graphs
Equi, Massimo
1
https://orcid.org/0000-0001-8609-0040
Meijer-van de Griend, Arianne
1
https://orcid.org/0000-0001-5946-0958
Mäkinen, Veli
1
https://orcid.org/0000-0003-4454-1493
Department of Computer Science, University of Helsinki, Finland
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(n²/w) time. In a reasonable classical model of computation, one can assume w = Θ(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-ε)) or O(|P|^(1-ε)|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|√|P|).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol259-cpm2023/LIPIcs.CPM.2023.9/LIPIcs.CPM.2023.9.pdf
Bit-parallelism
quantum computation
string matching
level DAGs