  Simulation of quantum matters is a significant application of quantum
computers. In contrast to the unitary operation which can be realized naturally
on a quantum computer, the implementation of nonunitary operation, widely used
in classical approaches, needs special designing. Here, by application of
Grover's algorithm, we extend the probabilistic method of implementing
nonunitary operation and show that it can promote success probability without
fidelity decreasing. This method can be applied to problems of imaginary time
evolution and contraction of tensor networks on a quantum computer.
