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Theoretical schemes for the implementation of the Grover search algorithm are proposed based on ultracold polar molecules in an electric field. The molecular qubits and qudit are chosen as the field‐dressed states formed by the rotational modes of CH3CN. With the help of multi‐target optimal control theory, the microwave pulses for the elementary logic operations including the one‐qubit Hadamard gates and the conditional phase gates in a dipole‐dipole system are designed and the factorized Grover algorithm demonstrated using two coupled CH3CN molecules. To reduce the accumulation of imprecision and decoherence resulting from the combination of multiple elementary gates, the optimal pulses that can achieve the two‐qubit Hadamard gate and diffusion operation in one step are designed successfully. In this way, the probabilities to find the states corresponding to the desired elements in an unsorted database are enhanced to some extent. Moreover, the optimal pulse sequence suitable for a four‐level molecular qudit, which can be used to simulate the quantum search on a single CH3CN molecule with high fidelity, is designed. These results can shed some light on the physical realization of quantum computing based on ultracold polyatomic molecules.

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