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Recent advancements in quantum technologies, particularly in quantum sensing and simulation, have facilitated the generation and analysis of inherently quantum data. This progress underscores the necessity for developing efficient and scalable quantum data management strategies. This goal faces immense challenges due to the exponential dimensionality of quantum data and its unique quantum properties such as no-cloning and measurement stochasticity. Specifically, classical storage and manipulation of an arbitrary n-qubit quantum state requires exponential space and time. Hence, there is a critical need to revisit foundational data management concepts and algorithms for quantum data. In this paper, we propose succinct quantum data sketches to support basic database operations such as search and selection. We view our work as an initial step towards the development of quantum data management model, opening up many possibilities for future research in this direction. 

In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated statistics like functional dependencies and degree constraints. Each new statistic prompted work along two lines; bounding the size of conjunctive query outputs and worst-case optimal join algorithms. In this work, we continue in this vein by introducing a new statistic called a partition constraint. This statistic captures latent structure within relations by partitioning them into sub-relations which each have much tighter degree constraints. We show that this approach can both refine existing cardinality bounds and improve existing worst-case optimal join algorithms. 

Recent work in programming languages developed an approach to term rewritings based on equality saturation (EqSat), which, instead of applying destructively the rewrite rules, maintains all equivalent expressions in a structure called an E-graph. This paper describes two surprising connections between EqSat and databases, going both ways. On one hand equality saturation can be viewed as a query evaluation problem, with great benefits. On the other hand, most sophisticated SQL query optimizers are based on the Volcano/Cascades framework which, we explain, is a variant of EqSat. 

Equality saturation is an emerging technique for program and query optimization developed in the programming language community. It performs term rewriting over an E-graph, a data structure that compactly represents a program space. Despite its popularity, the theory of equality saturation lags behind the practice. In this paper, we define a fixpoint semantics of equality saturation based on tree automata and uncover deep connections between equality saturation and the chase. We characterize the class of chase sequences that correspond to equality saturation. We study the complexities of terminations of equality saturation in three cases: single-instance, all-term-instance, and all-E-graph-instance. Finally, we define a syntactic criterion based on acyclicity that implies equality saturation termination. 

Decision makers in a broad range of domains, such as finance, transportation, manufacturing, and healthcare, often need to derive optimal decisions given a set of constraints and objectives. Traditional solutions to such constrained optimization problems are typically application-specific, complex, and do not generalize. Further, the usual workflow requires slow, cumbersome, and error-prone data movement between a database, and predictive-modeling and optimization packages. All of these problems are exacerbated by the unprecedented size of modern data-intensive optimization problems. The emerging research area of in-database prescriptive analytics aims to provide seamless domain-independent, declarative, and scalable approaches powered by the system where the data typically resides: the database. Integrating optimization with database technology opens up prescriptive analytics to a much broader community, amplifying its benefits. We discuss how deep integration between the DBMS, predictive models, and optimization software creates opportunities for rich prescriptive-query functionality with good scalability and performance. Summarizing some of our main results and ongoing work in this area, we highlight challenges related to usability, scalability, data uncertainty, and dynamic environments, and argue that perspectives from data management research can drive novel strategies and solutions.