  Based on a coherent state representation of noise operator and an ensemble
averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109
(2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to
derive the equations for time evolution of {\it true} probability distribution
functions in $c$-number phase space. We extend the treatment to develop a
numerical method for generation of $c$-number noise with arbitrary correlation
and strength at any temperature, along with the solution of the associated
generalized quantum Langevin equation. The method is illustrated with the help
of a calculation of quantum mean first passage time in a cubic potential to
demonstrate quantum Kramers turnover and quantum Arrhenius plot.
