Rigorous convergence condition for quantum annealing

• URL: http://arxiv.org/abs/2207.12096v2
• Date: Mon, 7 Nov 2022 13:54:59 GMT
• Title: Rigorous convergence condition for quantum annealing
• Authors: Yusuke Kimura and Hidetoshi Nishimori
• Abstract summary: We derive a generic bound on the rate of decrease of transverse field for quantum annealing to converge to the ground state of a generic Ising model. Our theorem is based on a rigorous upper bound on the excitation probability in the infinite-time limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We derive a generic bound on the rate of decrease of transverse field for quantum annealing to converge to the ground state of a generic Ising model when quantum annealing is formulated as an infinite-time process. Our theorem is based on a rigorous upper bound on the excitation probability in the infinite-time limit and is a mathematically rigorous counterpart of a previously known result derived only from the leading-order term of the asymptotic expansion of adiabatic condition. Since our theorem gives a sufficient condition of convergence for a generic transverse-field Ising model, any specific problem may allow a better, faster, control of the coefficient.

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