2015/04/30 by Kazuya Kaneko, Hidetoshi Nishimori
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Adiabatic theorem #Convergence (economics) #Ground state #Markov process #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Schrödinger equation #Simulated annealing #Spectral Theory in Mathematical Physics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.7566/jpsj.84.094001
published as J. Phys. Soc. Jpn. 84, 094001 (2015) · 5 pages
openalex publication_date 2015/08/05 · arxiv created 2015/08/06 · arxiv updated 2015/08/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We formulate an adiabatic approximation for the imaginary-time Schroedinger equation. The obtained adiabatic condition consists of two inequalities, one of which coincides with the conventional adiabatic condition for the real-time Schroedinger equation, but the other does not. We apply this adiabatic approximation to the analysis of Markovian dynamics of the classical Ising model, which can be formulated as the imaginary-time Schr"odinger equation, to obtain an asymptotic formula for the probability that the system reaches the ground state in the limit of a long annealing time in simulated annealing. Using this form, we amend the theory of Somma, Batista, and Ortiz for a convergence condition for simulated annealing.