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- W3103487277 abstract "We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower bound for the spectral gap. We apply this algorithm to the quantum linear system problem (QLSP), and present two algorithms based on quantum adiabatic computing (AQC) and quantum Zeno effect respectively. Both algorithms prepare the final solution as a pure state, and achieves the near optimal $mathcal{widetilde{O}}(dkappalog(1/epsilon))$ query complexity for a $d$-sparse matrix, where $kappa$ is the condition number, and $epsilon$ is the desired precision. Neither algorithm uses phase estimation or amplitude amplification." @default.
- W3103487277 created "2020-11-23" @default.
- W3103487277 creator A5032069482 @default.
- W3103487277 creator A5073533398 @default.
- W3103487277 date "2020-11-11" @default.
- W3103487277 modified "2023-10-15" @default.
- W3103487277 title "Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems" @default.
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- W3103487277 doi "https://doi.org/10.22331/q-2020-11-11-361" @default.
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