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• W3205455864 abstract "Abstract Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan et al 2019 Quantum 4 296] found that the lowest resource costs were achieved by split-operator Trotterization combined with the fast-fermionic Fourier transform (FFFT) on an L × L lattice with length L = 2 k . On lattices with length L ≠ 2 k , Givens rotations can be used instead of the FFFT but lead to considerably higher resource costs. We present a new analytic approach to bounding the simulation error due to Trotterization that provides much tighter bounds for the split-operator FFFT method, leading to 16× improvement in error bounds. Furthermore, we introduce plaquette Trotterization that works on any size lattice and apply our improved error bound analysis to show competitive resource costs. We consider a phase estimation task and show plaquette Trotterization reduces the number of non-Clifford gates by a factor 5.5× to 9× (depending on the parameter regime) over the best previous estimates for 8 × 8 and 16 × 16 lattices and a much larger factor for other lattice sizes not of the form L = 2 k . In conclusion, we find there is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates." @default.
• W3205455864 created "2021-10-25" @default.
• W3205455864 creator A5018132307 @default.
• W3205455864 date "2021-11-18" @default.
• W3205455864 modified "2023-10-17" @default.
• W3205455864 title "Early fault-tolerant simulations of the Hubbard model" @default.
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• W3205455864 doi "https://doi.org/10.1088/2058-9565/ac3110" @default.
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