Quantum solvability of noisy linear problems by divide-and-conquer strategy
- Authors
- Song, Wooyeong; Lim, Youngrong; Jeong, Kabgyun; Ji, Yun-Seong; Lee, Jinhyoung; Kim, Jaewan; Kim, M. S.; Bang, Jeongho
- Issue Date
- Apr-2022
- Publisher
- IOP Publishing Ltd
- Keywords
- quantum algorithm; noisy linear problem; quantum-sample complexity
- Citation
- QUANTUM SCIENCE AND TECHNOLOGY, v.7, no.2, pp.1 - 8
- Indexed
- SCIE
SCOPUS
- Journal Title
- QUANTUM SCIENCE AND TECHNOLOGY
- Volume
- 7
- Number
- 2
- Start Page
- 1
- End Page
- 8
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/138990
- DOI
- 10.1088/2058-9565/ac51b0
- ISSN
- 2058-9565
- Abstract
- Noisy linear problems have been studied in various science and engineering disciplines. A class of `hard' noisy linear problems can be formulated as follows: Given a matrix A and a vector b constructed using a finite set of samples, a hidden vector or structure involved in b is obtained by solving a noise-corrupted linear equation Ax approximate to b + eta, where eta is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.
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