  We investigate the short time quantum critical dynamics in the imaginary time
relaxation processes of finite size systems. Universal scaling behaviors exist
in the imaginary time evolution and in particular, the system undergoes a
critical initial slip stage characterized by an exponent $\theta$, in which an
initial power-law increase emerges in the imaginary time correlation function
when the initial state has zero order parameter and vanishing correlation
length. Under different initial conditions, the quantum critical point and
critical exponents can be determined from the universal scaling behaviors. We
apply the method to the one- and two-dimensional transverse field Ising models
using quantum Monte Carlo simulations. In the one-dimensional case, we locate
the quantum critical point at $(h/J)_{c}=1.00003(8)$ \thirdrevise{in the
thermodynamic limit}, and estimate the critical initial slip exponent
$\theta=0.3734(2)$, static exponent $\beta/\nu=0.1251(2)$ \thirdrevise{by
analyzing data on chains of length $L=32\sim 256$ and $L=48\sim 256$,
respectively}. For the two-dimensional square-lattice system, the critical
coupling ratio is given by $3.04451(7)$ \thirdrevise{in the thermodynamic
limit} while the critical exponents are \thirdrevise{$\theta=0.209(4)$ and
$\beta/\nu=0.518(1)$ estimated by data on systems of size $L=24\sim 64$ and
$L=32\sim 64$, correspondingly.} Remarkably, the critical initial slip
exponents obtained in both models are notably distinct from their classical
counterparts, owing to the essential differences between classical and quantum
dynamics. The short time critical dynamics and the imaginary time relaxation
QMC approach can be readily adapted to various models.
