Quantum divide and conquer
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913939255721984 |
|---|---|
| author | Childs, Andrew M. Kothari, Robin Kovacs-Deak, Matt Sundaram, Aarthi Wang, Daochen |
| author_facet | Childs, Andrew M. Kothari, Robin Kovacs-Deak, Matt Sundaram, Aarthi Wang, Daochen |
| contents | 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 $C^{\textrm{aux}}(n)$, to give a recurrence relation $$C(n) \leq a \, C(n/b) + C^{\textrm{aux}}(n)$$ for the classical complexity $C(n)$. We describe a quantum divide-and-conquer framework that, in certain cases, yields an analogous recurrence relation $$C_Q(n) \leq \sqrt{a} \, C_Q(n/b) + O(C^{\textrm{aux}}_Q(n))$$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06419 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum divide and conquer Childs, Andrew M. Kothari, Robin Kovacs-Deak, Matt Sundaram, Aarthi Wang, Daochen Quantum Physics Data Structures and Algorithms 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 $C^{\textrm{aux}}(n)$, to give a recurrence relation $$C(n) \leq a \, C(n/b) + C^{\textrm{aux}}(n)$$ for the classical complexity $C(n)$. We describe a quantum divide-and-conquer framework that, in certain cases, yields an analogous recurrence relation $$C_Q(n) \leq \sqrt{a} \, C_Q(n/b) + O(C^{\textrm{aux}}_Q(n))$$ 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. |
| title | Quantum divide and conquer |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2210.06419 |