  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.
