Polynomial-Time Algorithm for Simulation of Weakly Interacting Quantum Spin Systems |
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Authors: | Sergey Bravyi David DiVincenzo Daniel Loss |
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Affiliation: | (1) IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA;(2) Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland |
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Abstract: | We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial in n and δ−1, where n is the number of qubits, and δ is the required precision. Specifically, we consider Hamiltonians of the form , where H 0 describes non-interacting qubits, V is a perturbation that involves arbitrary two-qubit interactions on a graph of bounded degree, and is a small parameter. The algorithm works if is below a certain threshold value that depends only upon the spectral gap of H 0, the maximal degree of the graph, and the maximal norm of the two-qubit interactions. The main technical ingredient of the algorithm is a generalized Kirkwood-Thomas ansatz for the ground state. The parameters of the ansatz are computed using perturbative expansions in powers of . Our algorithm is closely related to the coupled cluster method used in quantum chemistry. |
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