Seminar: Andrew Childs (University of Maryland): "Quantum divide and conquer"

Speaker: Andrew Childs (University of Maryland)
Title: Quantum divide and conquer
Abstract: The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem into smaller subproblems, along with some auxiliary work, to give a recurrence relation for the classical complexity. We describe a quantum divide-and-conquer framework that, in certain cases, yields quantum speedup through an analogous recurrence relation for 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.

Based on joint work with Robin Kothari, Matt Kovacs-Deak, Aarthi Sundaram, and Daochen Wang (arXiv:2210.06419).