Abstract: To enhance the optimization ability of the cuckoo search algorithm, we propose a new quantum-inspired cuckoo search algorithm by studying the implementation mechanism of the cuckoo search algorithm. The bird's nest location in the algorithm is encoded by the quantum bits with double chains. To ensure uniform distribution of the individuals of the initial population, the quantitatively orthogonal strategy is introduced and the solution space is divided into subspaces. The size of the quantum rotation angle is achieved by Lévy flights random walk. It executes the quantitatively orthogonal crossover operation with the individuals that are discovered and mutated by Pauli-Z. The local refinement search is achieved in the orthogonal region. Simulation results of the functions' extreme value optimization indicate that the proposed algorithm is more efficient at optimization than the standard cuckoo search algorithm. The proposed algorithm is applied to the inversion problem of shale oil multi-mineral component content, and inversion accuracy is increased by approximately 6 percent.