In terms of the stochastic process of quantum Monte Carlo method, we analytically derive macroscopically deterministic flow equations of order parameters such as spontaneous magnetization in infinite-range quantum spin systems [1]. By means of the Suzuki-Trotter decomposition, we consider the transition probability of glauber-type dynamics of microscopic states for the corresponding (d+1)-dimensional classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the Master equation that describes the microscopic-law. In the steady state, the equations are identical to the saddle point equations for the equilibrium state of the same system. The equation for the dynamical Ising model is recovered in the classical limit. We also check the validity of the static approximation by making use of computer simulations for finite size systems. We also discuss several possible applications of our approach to several research areas, say, statistical-mechanical informatics [1] and neural networks [2].

[1]J. Inoue, Journal of Physics: Conference Series 233, 012010 (2010).

[2]J. Inoue, Journal of Physics: Conference Series 297, 012012 (2011).