Quantum divide and conquer

TitleQuantum divide and conquer
Publication TypeJournal Article
Year of Publication2022
AuthorsChilds, AM, Kothari, R, Kovacs-Deak, M, Sundaram, A, Wang, D
Date Published10/12/2022
KeywordsData Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)

The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size n into smaller subproblems (say, a copies of size n/b each), along with some auxiliary work of cost Caux(n), to give a recurrence relation
for the classical complexity C(n). We describe a quantum divide-and-conquer framework that, in certain cases, yields an analogous recurrence relation
that characterizes the quantum query complexity. We apply this framework to obtain near-optimal quantum query complexities for various string problems, such as (i) recognizing regular languages; (ii) decision versions of String Rotation and String Suffix; and natural parameterized versions of (iii) Longest Increasing Subsequence and (iv) Longest Common Subsequence.