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Given a large dataset of many tuples, it is hard for users to pick out their preferred tuples. Thus, the preference query problem, which is to find the most preferred tuples from a dataset, is widely discussed in the database area. In this problem, a utility function is given by the user to evaluate to what extent the user prefers a tuple. However, considering a dataset consisting of N tuples, the existing algorithms need O(N) time to answer a query, or need O(N) time for a cold start to answer a query. The reason is that in a classical computer, a linear time is needed to evaluate the utilities by the utility function for N tuples. In this paper, we discuss the Quantum Preference Query (QPQ) problem, where the dataset is given in a quantum memory, and we use a quantum computer to return the answers. Due to quantum parallelism, the quantum algorithm can theoretically perform better than their classical competitors. We discuss this problem in different kinds of input and output. In the QPQ problem, the input can be a number k or a threshold theta. Given k, the problem is to return k tuples with the highest utilities. Given theta, the problem is to return all the tuples with utilities higher than theta. Also, in QPQ problem, the output can be classical (i.e., a list of tuples) or quantum (i.e., a superposition in quantum bits). We proposed four quantum algorithms to solve the problems in the above four scenarios. We analyze the number of memory accesses needed for each quantum algorithm, which shows that the proposed quantum algorithms are at least quadratically faster than their classical competitors. In our experiments, we show that to answer a QPQ problem, the quantum algorithms achieve up to 1000x improvement in number of memory accesses than their classical competitors, which proved that QPQ problem could be a future direction of the study of preference query problems.

Quantum computing is a popular topic in computer science, which has recently attracted many studies in various areas such as machine learning and network. However, the topic of quantum data structures seems neglected. There is an open problem in the database area: Can we improve existing data structures by quantum techniques? Consider a dataset of key-record pairs. Given an interval as a query range, a classical B+ tree can report all the records with keys within this interval, which is called a range query, in O(log N + k) time, where N is the total number of records and k is the output size. It is asymptotically optimal in a classical computer but not efficient enough in a quantum computer, because it is expected that the execution time and the output size are linear in a quantum computer. In this paper, we propose the quantum range query problem. Different from the classical range queries, a quantum range query returns the results in quantum bits, which has broad potential applications due to the foreseeable advance of quantum computers and quantum algorithms. To the best of our knowledge, we design the first tree-like quantum data structure called the quantum B+ tree. Based on this data structure, we propose a hybrid quantum-classical algorithm to do the range search. It answers a static quantum range query in O(log_B N) time, which is asymptotically optimal in quantum computers. Since the execution time does not depend on the output size (i.e., k, which could be as large as O(N)), it is significantly faster than the classical data structure. Moreover, we extend our quantum B+ tree to answer the dynamic and d-dimensional quantum range queries efficiently in O(log^2_B N) and O(log^d_B N) time, respectively. Our experimental results show that our proposed quantum data structures achieve up to 1000x improvement in the number of memory accesses compared to their classical competitors.