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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Quantum simulation of electronic structure via quantum fast multipole method
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.