Left-Deep Join Order Selection with Higher-Order Unconstrained Binary Optimization on Quantum Computers

Valter Uotila^*

• University of Helsinki, Helsinki, Finland

Join order optimization is among the most crucial query optimization problems, and its central position is also evident in the new research field where quantum computing is applied to database optimization and data management. In the field, join order optimization is the most studied database problem, typically tackled with a quadratic unconstrained binary optimization model, which is solved using various meta-heuristics, such as quantum and digital annealing, the quantum approximate optimization algorithm, or the variational quantum eigensolver. In this work, we continue developing quantum computing techniques for left-deep join order optimization by presenting three novel quantum optimization algorithms. These algorithms are based on a higher-order unconstrained binary optimization model, which is a generalization of the quadratic model and has not previously been applied to database problems. Theoretically, these optimization problems naturally map to universal quantum computers and quantum annealers. Compared to previous research, two of our algorithms are the first quantum algorithms to model the join order cost function precisely. We prove theoretical bounds by showing that these two methods encode the same plans as the dynamic programming algorithm with respect to the query graph, which provides the optimal result up to cross-products. The third algorithm achieves plans at least as good as those of the greedy algorithm with respect to the query graph. These results establish a meaningful theoretical connection between classical and quantum algorithms for selecting left-deep join orders. To demonstrate the practical usability of our algorithms, we have conducted an extensive experimental evaluation on thousands of clique, cycle, star, tree, and chain query graphs using both quantum and classical solvers.