Quantum solvability of noisy linear problems by divide-and-conquer strategy

نویسندگان

چکیده

Abstract Noisy linear problems have been studied in various science and engineering disciplines. A class of ‘hard’ noisy can be formulated as follows: Given a matrix A ^ vector b constructed using finite set samples, hidden or structure involved is obtained by solving noise-corrupted equation $\hat{A}\mathbf{x}\approx \mathbf{b}+\boldsymbol{\eta }$?> x ≈ mathvariant="bold">b + mathvariant="bold-italic">η , where η noise that cannot identified. For such problem, we consider quantum algorithm based on divide-and-conquer strategy, wherein large core process divided into smaller subprocesses. The appropriately reduces both the computational complexities size sample. More specifically, if computer access particular reduced form polynomial quantum-sample time are achieved main computation. sample its executing system reduced, e.g., from exponential to sub-exponential with respect problem length, which better than other results aware. We analyse model conditions for advantage, show when strategy beneficial problems.

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ژورنال

عنوان ژورنال: Quantum science and technology

سال: 2022

ISSN: ['2364-9054', '2364-9062']

DOI: https://doi.org/10.1088/2058-9565/ac51b0