Ready to Leap (by Co-Design)? Join Order Optimisation on Quantum Hardware

Abstract

The prospect of achieving computational speedups by exploiting quantum phenomena makes the use of quantum processing units (QPUs) attractive for many algorithmic database problems. Query optimisation, which concerns problems that typically need to explore large search spaces, seems like an ideal match for quantum algorithms. We present the first quantum implementation of join ordering, one of the most investigated and fundamental query optimisation problems, based on a reformulation to quadratic binary unconstrained optimisation problems. We empirically characterise our method on two state-of-the-art approaches (gate-based quantum computing and quantum annealing), and identify speed-ups compared to the best know classical join ordering approaches for input sizes conforming to current quantum annealers. Yet, we also confirm that limits of early-stage technology are quickly reached. Current QPUs are classified as noisy, intermediate scale quantum computers (NISQ), and are restricted by a variety of limitations that reduce their capabilities as compared to ideal future QPUs, which prevents us from scaling up problem dimensions and reaching practical utility. To overcome these challenges, our formulation accounts for specific QPU properties and limitations, and allows us to trade between achievable solution quality and problem size. In contrast to all prior work on quantum computing for query optimisation and database-related challenges, we go beyond currently available QPUs, and explicitly target the scalability limitations: Using insights gained from numerical simulations and our experimental analysis, we identify key criteria for co-designing QPUs to improve their usefulness for join ordering, and show how even relatively minor physical architectural improvements can result in substantial enhancements. Finally, we outline a path towards practical utility of custom-designed QPUs.