  Simulated quantum annealing is a generic classical protocol to simulate some
aspects of quantum annealing and is sometimes regarded as a classical
alternative to quantum annealing in finding the ground state of a classical
Ising model. We derive a generic condition for simulated quantum annealing to
converge to thermal equilibrium at a given, typically low, temperature. Both
closed and open systems are treated. We rewrite the classical master equation
for simulated quantum annealing into an imaginary-time Schr\"odinger equation,
to which we apply the imaginary-time variant of asymptotic adiabatic condition
to deduce the convergence condition. The result agrees qualitatively with a
rigorous convergence condition of simulated quantum annealing for closed
systems, which was derived from the theory of inhomogeneous Markov process.
Also observed is qualitative agreement with a rigorous convergence condition of
quantum annealing for closed systems under the real-time Schr\"odinger
dynamics. This coincidence of convergence conditions for classical stochastic
processes for simulated quantum annealing and the real-time quantum dynamics
for quantum annealing is highly non-trivial and calls for further scrutiny.
