Quantum Preference Query

TL;DR

The paper tackles the problem of identifying user-favored tuples from a multi-attribute dataset by leveraging quantum memory and quantum computation. It formalizes the Quantum Preference Query (QPQ) across four scenarios (top-$k$ or threshold inputs, classical or quantum outputs) and introduces four corresponding quantum algorithms that exploit QRAM, amplitude amplification, and post-selection to achieve at least quadratic speedups in memory-access complexity. Theoretical analyses establish IO complexities of $O\left(\sqrt{\frac{N}{k}}\right)$ or $O(\sqrt{Nk})$ in various settings, often outperforming the best classical approaches by substantial factors, and empirical simulations report up to 1000x improvements in memory accesses. The work demonstrates the potential of quantum-accelerated preference queries for large-scale decision-support tasks and sketches directions for adapting these techniques to broader database-analytics problems.

Abstract

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.

Figures (7)

• Figure 1: Post-selection on $\mathcal{O}_5$
• Figure 2: An illustration of the quantum circuit for QQPQ$_\theta$
• Figure 3: The Effect of $k$ for the CQPQ$_k$ Queries
• Figure 4: The Effect of $d$, $N$ and dataset category for the CQPQ$_k$ Queries
• Figure 5: The Effect of $k$ for the CQPQ$_{\theta}$ Queries

Theorems & Definitions (13)

• definition 1: Quantum Random Access Memory (QRAM)
• definition 2: Classical-Output Threshold-Based Quantum Preference Query (CQPQ$_\theta$)
• definition 3: Quantum-Output Threshold-Based Quantum Preference Query (QQPQ$_\theta$)
• definition 4: Classical-Output Top-$k$ Quantum Preference Query (CQPQ$_k$)
• definition 5: Quantum-Output Top-$k$ Quantum Preference Query (QQPQ$_k$)
• theorem 1
• proof
• theorem 2
• proof
• lemma 1