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We study the imaginary-time relaxation critical dynamics of a quantum systemwith a vanishing initial correlation length and an arbitrary initial orderparameter $M_0$. We find that in quantum critical dynamics, the behavior of$M_0$ under scale transformations deviates from a simple power-law, which wasproposed for very small $M_0$ previously. A universal characteristic functionis then suggested to describe the rescaled initial magnetization, similar toclassical critical dynamics. This characteristic function is shown to be ableto describe the quantum critical dynamics in both short- and long-time stagesof the evolution. The one-dimensional transverse-field Ising model is employedto numerically determine the specific form of the characteristic function. Wedemonstrate that it is applicable as long as the system is in the vicinity ofthe quantum critical point. The universality of the characteristic function isconfirmed by numerical simulations of models belonging to the same universalityclass.

Generalized dynamic scaling for quantum critical relaxation in imaginary time