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Simulation of quantum matters is a significant application of quantumcomputers. In contrast to the unitary operation which can be realized naturallyon a quantum computer, the implementation of nonunitary operation, widely usedin classical approaches, needs special designing. Here, by application ofGrover's algorithm, we extend the probabilistic method of implementingnonunitary operation and show that it can promote success probability withoutfidelity decreasing. This method can be applied to problems of imaginary timeevolution and contraction of tensor networks on a quantum computer.

Probabilistic Nonunitary Gate in Imaginary Time Evolution