Convergence of Quantum Annealing with Real-Time Schrodinger Dynamics(General)
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概要
- 論文の詳細を見る
Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et al. for the analysis of classical simulated annealing using a classical-quantum correspondence.
- 社団法人日本物理学会の論文
- 2007-06-15
著者
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Morita Satoshi
Department Of Biostatistics And Epidemiology Yokohama City University Medical Center
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Nishimori Hidetoshi
Department Of Physics Tokyo Institute Of Technology
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Morita Satoshi
Department Of Physics Tokyo Institute Of Technology
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Nishimori Hidetoshi
Department Of Physics Facuilty Of Science Tokyo Institute Of Technology
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Morita Satoshi
Department Of Biostatistics And Epidemiology Yokohama City University Graduate School Of Medicine
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MORITA Satoshi
Department of Biostastics and Epidemiology, Yokohama City University Medical Center
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