  We study the effects of dissipation or leakage on the time evolution of
Grover's algorithm for a quantum computer. We introduce an effective two-level
model with dissipation and randomness (imperfections), which is based upon the
idea that ideal Grover's algorithm operates in a 2-dimensional Hilbert space.
The simulation results of this model and Grover's algorithm with imperfections
are compared, and it is found that they are in good agreement for appropriately
tuned parameters. It turns out that the main features of Grover's algorithm
with imperfections can be understood in terms of two basic mechanisms, namely,
a diffusion of probability density into the full Hilbert space and a stochastic
rotation within the original 2-dimensional Hilbert space.
