关键词: 量子联想分类器, 均衡叠加态, Hamming距离, 量子最小搜索

Abstract: Aiming at the problem that the existing associative classifier could not store duplicate samples, we proposed  a design method of associative classifier based on Hamming distance and quantum search algorithm, and gave a line diagram for the storage and classification of the associative classifier. The method required the preparation of  five sets of qubits  in advance to encode Hamming distance, input sample, pattern sample, category and sequence number respectively. Firstly, according to the total N of the sample, the number of qubits required by the associative classifier was calculated, and then the qubits with an  initial state of  |0〉were rotated to an equilibrium superposition state containing exactly N ground states by using the quantum revolving gate and the Hadamard gate. Secondly, according to the category and value of the sample to be stored, the remaining two sets of qubits with initial state of  |0〉 were converted into the corresponding quantum ground state through controllable operation. Finally, based on the classification method of quantum minimum search, the Hamming distance between the input sample and all the stored samples was calculated, and then the fixed phase Grover quantum search algorithm was used to search for the minimum value of these Hamming distances.  The category of the stored sample corresponding to the minimum value was the category of the input sample, and the specific classification results could be obtained by measuring the quantum states in the register.

Key words: quantum associative classifier, equilibrium superposition state, Hamming distance, quantum minimum search