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Journal Article
Quantum Solvability of Noisy Linear Problems by Divide-and-conquer Strategy
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- Authors
- Wooyeong Song, Youngrong Lim, Kabgyun Jeong, Yun-Seong Ji, Jinhyoung Lee, Jaewan Kim, M S Kim, Jeongho Bang
- Issue Date
- 2022-04
- Citation
- Quantum Science and Technology, v.7, no.2, pp.1-8
- ISSN
- 2058-9565
- Publisher
- Institute of Physics (IOP)
- Language
- English
- Type
- Journal Article
- 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≈b+η, where η 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.
- KSP Keywords
- Divide-and-conquer, Engineering disciplines, Large core, Linear equations, Reduced form, linear problem, noise models, quantum algorithm, quantum computer