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- W4296984701 abstract "We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multiscale hyperbolic heat system with quantum algorithms (hence referred to as the quantum difference methods). For the heat and linear hyperbolic equations we study the impact of explicit and implicit time discretizations on quantum advantages over the classical difference method. For the multiscale problem, we find the time complexity of both the classical treatment and quantum treatment for the explicit scheme scales as $mathcal{O}(1/varepsilon)$, where $varepsilon$ is the scaling parameter, while the scaling for the multiscale Asymptotic-Preserving (AP) schemes does not depend on $varepsilon$. This indicates that it is still of great importance to develop AP schemes for multiscale problems in quantum computing." @default.
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- W4296984701 date "2022-12-01" @default.
- W4296984701 modified "2023-09-29" @default.
- W4296984701 title "Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations" @default.
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- W4296984701 doi "https://doi.org/10.1016/j.jcp.2022.111641" @default.
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