Given a query plan, the goal of multiobjective query optimization [1] is to optimally map each operator in a plan to an implementation. Operator implementations differ by quality metrics such as cost and latency. In this context, query optimization becomes a multiobjective optimization problem. The optimal solution depends on user preferences and minimizes, for instance, a weighted sum over different cost metrics. We show how to transform instances of multiobjective query optimization, an NP-hard problem [1], into equivalent Quadratic Unconstrained Binary Optimization (QUBO) formulas that can be solved efficiently on quantum annealers.
Given a query plan, the goal of multiobjective query optimization [1] is to optimally map each operator in a plan to an implementation. Operator implementations differ by quality metrics such as cost and latency. In this context, query optimization becomes a multiobjective optimization problem. The optimal solution depends on user preferences and minimizes, for instance, a weighted sum over different cost metrics. We show how to transform instances of multiobjective query optimization, an NP-hard problem [1], into equivalent Quadratic Unconstrained Binary Optimization (QUBO) formulas that can be solved efficiently on quantum annealers.
Abstract : One approach to solving planning problems is to compile them to another problem for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances encoded as Quadratic Unconstrained Binary Optimization (QUBO). Early quantum annealers are now available, and more sophisticated quantum annealers will likely be built over the next decades. Specific quantum annealing hardware implementations have specific constraints, restricting the types of QUBOs each can take as input. In this paper, we introduce the planning community to the key steps involved in compiling planning problems to quantum annealing hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we provide preliminary results from running an early quantum annealer on a parameterized family of hard planning problems. The results show that different mappings can lead to a substantial difference in performance, even when many superficial features of the resulting instances are similar. We also provide some insights gained from this early study, and suggest directions for future work.
Abstract One approach to solving planning problems is to compile them to other problems for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.
The increasing complexity of computational problems in various fields entails the development of efficient methods to solve them. Thus, the emerging technology of quantum computers comes with algorithms, such as quantum annealing, that could solve optimization problems exponentially faster. In particular, to solve the 3SAT problem on quantum annealers, it must be transformed into an instance of Quadratic Unconstrained Binary Optimization (QUBO). Given that the choice of 3SAT-to-QUBO transformation affects the solution quality on quantum annealing, an algorithmic method for creating numerous 3SAT-to-QUBO transformations has recently been proposed, aiming to investigate more deeply such effect. This represents a challenge when deciding which is the best performing 3SAT-to-QUBO transformation that should be used when solving a 3SAT instance on quantum annealing. To overcome this issue, this work investigates the impact of different 3SAT-to-QUBO transformations on the solution quality of simulated annealing, as a classical analogue to quantum annealing. We demonstrate that different QUBO encodings of the same 3SAT instance can lead to different outcomes in terms of energy and clause satisfaction. We also reveal some correlations between 3SAT features, QUBO structural properties, and solution quality. These findings underscore the importance of the choice of 3SAT-to-QUBO transformation in simulated annealing, and provide a foundation for the future development of machine learning models for guiding encoding choices in both classical and quantum environments.
Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.
The rapidly increasing number of heterogeneous data ecosystems, such as structured databases, semi-structured data lakes, real-time streams, distributed knowledge graphs, has further complicated the issue of query planning and optimization in modern information systems extensively. The optimization of queries is essentially an NP-hard combinatorial problem especially when based on multi-join queries, distributed execution plan, dynamic cost model, and uncertainty in the data access patterns. Even decades of concept and engineering advances, classical database optimizers are rapidly becoming unable to offer a globally optimal execution plan when faced with high-dimensional data, high data volatility, with a very tight latency constraint. Good news Recent breakthroughs in quantum computing propose promising computational paradigms that can be used to solve combinatorial optimization problems via quantum parallelism, superposition, and entanglement. Nevertheless, even the near-term quantum hardware is limited in the number of available qubits, noise, and decoherence, making it impractical to achieve fully quantum database systems in any perceived future. This is also the reason why quantum-classical hybrid algorithms are being developed: designed to add quantum optimization subroutines to classical database architectures is guaranteed without breaking their compatibility with existing execution engines. The following paper presents a framework of scalable quantum-classical hybrid computing of complex query planning in heterogeneous data ecosystems. The framework breaks down query optimization into classical and quantum-amenable optimization, which allows NP-hard subproblems, such as join ordering, operator placement, and cost minimization, to be transformed into quantum optimization models such as Quadratic Unconstrained Binary Optimization (QUBO) and Ising Hamiltonians. Classical elements handle query parsing, semantic analysis, constraint verification, and orchestration, whereas quantum processors are called selectively to solve combinatorial decision-making tasks. The suggested architecture will consist of a layered execution, hybrid execution, cost-model encoding approach, and adaptive fallback mechanisms to make them robust to quantum hardware variability. This has been experimentally tested with simulated quantum annealing and variational quantum algorithms that exhibit a quantifiable improvement in the quality and scalability of optimization and heuristics based on entirely classical algorithms, especially in high-dimensional query plans. The findings confirm the practicability of quantum query optimization and put down a feasible route to implement quantum algorithms in the serving machine of the next-generation data management systems.
To solve 3sat instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3sat problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.