Quantum fast multipole method yields electronic structure simulation gate complexity t(η^{4/3}N^{1/3} + η^{1/3}N^{2/3})(η N t / ε)^{o(1)}, providing roughly O(η) speedup over prior work for N < η^7.
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ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.
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Estimating Green's functions with a robust quantum Arnoldi method
ROQAM formulates Green's function estimation via orthogonal polynomials to preserve Hessenberg structure under finite precision, enabling lower precision with depth and outperforming QSVD by orders of magnitude in resource estimates for a quantum impurity model.