Adiabatic approximation for the imaginary-time Schroedinger equation and its application to simulated annealing

Abstract

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 Schrödinger 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.

5 pages

References in corpus (3)

• Mathematical Foundation of Quantum Annealing
• A Quantum Approach to Classical Statistical Mechanics
• Comparative Study of the Performance of Quantum Annealing and Simulated Annealing

Cited by in corpus (4)

• Constant-adiabaticity RF-pulses for generating long-lived singlet spin states in NMR
• Constant-adiabaticity ultralow magnetic field manipulations of parahydrogen-induced polarization: application to an AA'X spin system
• Quantum annealing speedup over simulated annealing on random Ising chains
• Difference between quantum annealing by imaginary-time and real-time Schrödinger equation of Grover's search