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Abstract: We describe an algorithm that computes the ground state energy andcorrelation functions for 2-local Hamiltonians in which interactions betweenqubits are weak compared to single-qubit terms. The running time of thealgorithm is polynomial in the number of qubits and the required precision.Specifically, we consider Hamiltonians of the form $H=H 0+\epsilon V$, whereH 0 describes non-interacting qubits, V is a perturbation that involvesarbitrary two-qubit interactions on a graph of bounded degree, and $\epsilon$is a small parameter. The algorithm works if $|\epsilon|$ is below a certainthreshold value that depends only upon the spectral gap of H 0, the maximaldegree of the graph, and the maximal norm of the two-qubit interactions. Themain technical ingredient of the algorithm is a generalized Kirkwood-Thomasansatz for the ground state. The parameters of the ansatz are computed usingperturbative expansions in powers of $\epsilon$. Our algorithm is closelyrelated to the coupled cluster method used in quantum chemistry.



Autor: Sergey Bravyi, David DiVincenzo, Daniel Loss

Fuente: https://arxiv.org/







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