Quantum algorithm for association rules mining

Association rules mining is one of the most important problems in knowledge discovery and data mining. The goal of it is to acquire consumption habits of customers by discovering the relationships between items from a transaction database that has a large number of transactions and items. The most compute intensive process for ARM is to find out the frequent 1-itemsets and 2-itemsets. In this paper, we propose a quantum algorithm for finding out the frequent 1-itemsets and 2-itemsets. In our algorithm, to mine the frequent 1-itemsets efficiently, we use the technique of amplitude amplification. To mine the frequent 2-itemsets efficiently, we propose a new tomography scheme, i.e., pure-state-based quantum state tomography. It is shown that our algorithm is potential to achieve exponential speedup in the number of transactions and polynomial speedup in the number of items over the classical algorithm.