In order to solve the high time complexity problem of the adversarial example detection algorithm based on Local Intrinsic Dimensionality （LID）， combined with the advantages of quantum computing， an adversarial example detection algorithm based on quantum LID was proposed. First， the SWAP-Test quantum algorithm was used to calculate the similarity between the measured example and all examples in one time， avoiding the redundant calculation in the classical algorithm. Then Quantum Phase Estimation （QPE） algorithm and quantum Grover search algorithm were combined to calculate the local intrinsic dimension of the measured example. Finally， LID was used as the evaluation basis of the binary detector to detect and distinguish the adversarial examples. The detection algorithm was tested and verified on IRIS， MNIST， and stock time series datasets. The simulation experimental results show that the calculated LID values can highlight the difference between adversarial examples and normal examples， and can be used as a detection basis to differentiate example attributes. Theoretical research proves that the time complexity of the proposed detection algorithm is the same order of magnitude as the product of the number of iterations of Grover operator and the square root of the number of adjacent examples and the number of training examples， which is obviously better than that of the adversarial example detection algorithm based on LID and achieves exponential acceleration.

The K-Means algorithms typically utilize Euclidean distance to calculate the similarity between data points when dealing with large-scale heterogeneous data. However， this method has problems of low efficiency and high computational complexity. Inspired by the significant advantage of Hamming distance in handling data similarity calculation， a Quantum K-Means Hamming （QKMH） algorithm was proposed to calculate similarity. First， the data was prepared and made into quantum state， and the quantum Hamming distance was used to calculate similarity between the points to be clustered and the K cluster centers. Then， the Grover’s minimum search algorithm was improved to find the cluster center closest to the points to be clustered. Finally， these steps were repeated until the designated number of iterations was reached or the clustering centers no longer changed. Based on the quantum simulation computing framework QisKit， the proposed algorithm was validated on the MNIST handwritten digit dataset and compared with various traditional and improved methods. Experimental results show that the F1 score of the QKMH algorithm is improved by 10 percentage points compared with that of the Manhattan distance-based quantum K-Means algorithm and by 4.6 percentage points compared with that of the latest optimized Euclidean distance-based quantum K-Means algorithm， and the time complexity of the QKMH algorithm is lower than those of the above comparison algorithms.