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• W3098796089 abstract "We consider an algorithm to approximate complex-valued periodic functions $f(e^{itheta})$ as a matrix element of a product of $SU(2)$-valued functions, which underlies so-called quantum signal processing. We prove that the algorithm runs in time $mathcal O(N^3 mathrm{polylog}(N/epsilon))$ under the random-access memory model of computation where $N$ is the degree of the polynomial that approximates $f$ with accuracy $epsilon$; previous efficiency claim assumed a strong arithmetic model of computation and lacked numerical stability analysis." @default.
• W3098796089 created "2020-11-23" @default.
• W3098796089 creator A5036464616 @default.
• W3098796089 date "2019-10-07" @default.
• W3098796089 modified "2023-10-17" @default.
• W3098796089 title "Product Decomposition of Periodic Functions in Quantum Signal Processing" @default.
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• W3098796089 doi "https://doi.org/10.22331/q-2019-10-07-190" @default.
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