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arXiv · 2408.01762

Investigation on a quantum algorithm for linear differential equations

Xiaojing Dong·Yizhe Peng·Qili Tang·Yin Yang·Yue Yu
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Abstract

Ref.[BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm.

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Xiaojing Dong, Yizhe Peng, Qili Tang, Yin Yang, Yue Yu. 2024-08-03. Investigation on a quantum algorithm for linear differential equations. https://arxiv.org/abs/2408.01762

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