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International Journal of Theoretical Physics

Design of Quantum Associative Classifier based on Hamming Distance and Grover’s Algorithm

Lingdong Meng, Ziyang Li, Panchi Li

Published Feb 2, 2024• 0 citations
Publisher
DOI
10.1007/s10773-024-05546-6

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In this paper, an algorithm of quantum associative memory is proposed using quantum search algorithms. In the associative memory, the problem is to find the data or the nearest data in the meaning of hamming distance from designated data. If the search data in memorized dataset is contained, the problem becomes data search one. In associative memory, it is difficult to find the nearest data in hamming distance. For searching any item in an unsorted database with N items, a classical takes O(N) steps but Grover’s quantum searching algorithm takes only O( p N) steps on perfect graph. By generalizing the idea, Ventura has proposed the associative memory model, but it does not solve the problem of finding the nearest data. On the other hand, quantum search algorithm with O( p N) steps on hypercube is also proposed. Therefore, the idea in this paper is formalizing the problem as quantum search algorithm in hypercube but not in the conventional perfect graph. First, we perform quantum search algorithm by considering quantum walk on hypercube. Further, it is observed search data or the nearest data by using the conventional algorithm with high probability.
Abstract Traditional iris recognition method has low speed and searching rate under large-scale unstructured database background, it needs N/2 times to find the result when the database has N irises, and the probability of success is 1/2. An improved recognition method based on quantum parallelism and Grover quantum search algorithm is proposed. The feature vector's encoding and Hamming distance are extracted through twice calculations by using quantum parallelism. The Oracle operator in Grover algorithm is improved. The improved Oracle operator includes two databases. The database one contains four registers: index register, quantum bit register which includes target iris Hamming distance, data register, one quantum bit register. Database two includes all the Hamming distance. Compared with traditional recognition method, the proposed method just needs to apply N operations, the target iris location can be found from iris database. The simulation results show that the proposed method decreases the number of repetitions and effectively improves the search speed.