The join order is one of the most important factors that impact the speed of query processing. Its optimization is known to be NP-hard, such that it is worth investigating the benefits of utilizing quantum computers for optimizing join orders. Hence in this paper, we propose to model the join order problem as quadratic unconstrained binary optimization (QUBO) problem to be solved with various quantum approaches like QAOA, VQE, simulated annealing and quantum annealing. In this paper, we will show the enhanced performance using our QUBO formulation to find valid and optimal shots for real-world queries joining three, four and five relations on D-Wave quantum annealer. The highlight of this study will demonstrate that we were able to generate valid and optimal join orders for five relations using the D-Wave quantum annealer, with values of about 12% and 0.27% respectively and we were able to find the optimal bushy join trees. Experiments for the gate-based simulations were able to produce optimized join order for three and four relations including bushy trees using QAOA and VQE algorithms.
The join order is one of the most important factors that impact the speed of query processing. Its optimization is known to be NP-hard, such that it is worth investigating the benefits of utilizing quantum computers for optimizing join orders. Hence in this paper, we propose to model the join order problem as quadratic unconstrained binary optimization (QUBO) problem to be solved with various quantum approaches like QAOA, VQE, simulated annealing and quantum annealing. In this paper, we will show the enhanced performance using our QUBO formulation to find valid and optimal shots for real-world queries joining three, four and five relations on D-Wave quantum annealer. The highlight of this study will demonstrate that we were able to generate valid and optimal join orders for five relations using the D-Wave quantum annealer, with values of about 12% and 0.27% respectively and we were able to find the optimal bushy join trees. Experiments for the gate-based simulations were able to produce optimized join order for three and four relations including bushy trees using QAOA and VQE algorithms.
Abstract The join order has a huge impact on the execution time of a query, such that finding an optimal join order plays a crucial role in query optimization. However, join order optimization is known to be NP-hard. Hence, in this paper, we propose an approach for accelerating join order optimization by quantum computers. We extend our previous approach supporting bushy join trees by splitting the search space of possible join orders and solving each of these subspaces on currently available quantum computers to optimize the join of more relations than our previous approach. We have integrated our approach to quantum query optimization in the relational database management system PostgreSQL to conduct studies with real-world queries. In our experiments, we show that we can perform join order optimization up to 7 relations for real-world queries using quantum annealing and up to 8 relations for artificial queries using simulated annealing with a reasonable number of QUBO problems solved by D‑Wave’s Quantum Annealer. Furthermore, we show that our approach can be also used to perform join-order for queries joining five relations on circuit-based quantum computers running the quantum approximate optimization algorithm (QAOA) and variational quantum eigensolver (VQE) approaches.
Optimal join order sequence significantly impacts query execution performance.Because the search space grows exponentially with the number of relations involved in the queries, DP-based approaches can compute optimal plans only for queries with a small number of relations.Many heuristic methods trade off solution quality for computational efficiency.Quantum computing excels at solving combinatorial optimization problems such as join order optimization.However, existing quantum-related methods either focus solely on left-deep join trees-thus narrowing the problem scope-or support bushy join trees but are constrained by quantum hardware and cannot scale to large queries.Importantly, neither branch has been integrated into an actual database system.In this paper, we present a hybrid quantum-classical optimization approach for bushy join trees, integrated within a real database system (PostgreSQL).This approach expands the search space for join order sequences and overcomes previous limitations.Evaluation on the Join Order Benchmark shows that our method can reduce query execution time by up to 92.7% and achieve a 1.42x improvement in end-to-end latency.
Efficient query optimization is crucial for relational database systems, especially for optimizing join orders in complex queries. This work introduces a hybrid approach that integrates Eliminating Cartesian Products (ECP) with splitting the QUBO search space (SQSS) to reduce the size of the QUBO problem, minimizing binary variables and constraints. This improves the performance of the quantum algorithm while lowering hardware requirements. We evaluate our method using real-world SQL queries from the ErgastF1 dataset on quantum and classical algorithms, including Quantum Annealing (QA), Simulated Annealing (SA), QAOA, and VQE, implemented on D-Wave's Quantum Annealer and universal gate-based simulators. Additionally, we analyze the impact of selectivity and SQSS on QUBO weight distribution and algorithmic performance, highlighting optimization efficiency for QA and SA. Experimental results show consistent optimal join orders and enhanced query optimization for various selectivity conditions, and they also highlight the limitations of current quantum hardware for complex queries. This study further confirms the potential of hybrid quantum-classical methods for scalable quantum-enhanced database optimization.
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 this 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 study, 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 studies, 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.
Join Order Optimization (JOO) is one of the most computationally expensive tasks in relational query optimization due to the exponential growth of possible join plans with increasing query size. Recent work has explored quantum and quantum-inspired approaches for solving JOO by reformulating the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem suitable for optimization using quantum hardware. However, many existing approaches have limited scalability on current gate-based quantum devices. In addition, little work has investigated the role of initialization strategies in improving the performance of gate-based quantum optimization for database workloads. In this work, we investigate gate-based quantum join order optimization using the Quantum Approximate Optimization Algorithm (QAOA) initialized with Scalable Parameter Initialization for QAOA (SPIQ). SPIQ is used to efficiently identify high-quality initial points in the quantum solution landscape for QAOA executed on a gate-based quantum computer. We evaluate the interaction between QUBO encoding, SPIQ initialization, and gate-based optimization on small-scale join ordering problems involving 3 and 4 relations. Our results show that structured initialization improves optimization stability and increases convergence toward high-quality join plans compared to uninformed initialization approaches. Across these small-scale, simulation-based instances, SPIQ increases the sampling frequency of the optimal join order by up to approximately 5× and yields final-state energies significantly lower than a randomly initialized QAOA. Overall, this work enhances existing gate-based quantum optimization while providing an initial proof of concept for applying SPIQ initialization to database query optimization workloads.
Recent advancements in quantum computing have demonstrated significant potential for solving combinatorial optimization problems, like the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum and quantum-inspired algorithms often require transforming these constrained problems into an unconstrained form, known as Quadratic Unconstrained Binary Optimization (QUBO). Such transformations can significantly impact the algorithms’ speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess all nine methods using Simulated Annealing and find that three of our approaches outperform existing methods in terms of execution time and the quality and quantity of feasible solutions found. Additionally, we tested these transformations on quantum annealers, which were unable to solve even small problem instances, due to limitations in connectivity and error rates. However, our results highlight the advantages of the new approaches, which reduce the total number of variables in the QUBO representation. This is a critical factor for enhanced performance on emerging quantum hardware, since it also reduces the required number of qubits and the embedding chain lengths.