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Quantum divide and conquer · arXivDesk

2210.06419Oct 12, 202224 pages, 8 figures

Quantum divide and conquer

Andrew M. Childs, Robin Kothari, Matt Kovacs-Deak, Aarthi Sundaram, Daochen Wang

Quantum Physics Data Structures and Algorithms

Abstract

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 $C(n) \leq a \, C(n/b) + C^{\textrm{aux}}(n)$

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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^aux(n), to give a recurrence relation C(n) ≤ a C(n/b) + C^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) ≤ √a C_Q(n/b) + O(C^aux_Q(n)) that characterizes the quantum query complexity.

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Researchers working in quant-ph and adjacent areas.

Claims

The paper addresses: Quantum divide and conquer.
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^aux(n), to give a recurrence relation C(n) ≤ a C(n/b) + C^aux(n) for the classical complexity C(n).