A Toolbox to Understand the Physics of Quantum Data Management

The application of quantum computing to data management has attracted growing interest, yet remains constrained by a limited understanding of how the physical behaviour of quantum devices relates to the structure and difficulty of database problems. In particular, evaluating quantum annealing approaches for combinatorial optimisation, which is central to many data management tasks, poses significant challenges beyond the scope of conventional empirical and complexity-theoretic methods. This work addresses this gap by presenting a computational toolbox for the systematic numerical analysis of quantum annealing processes derived from data management problem formulations. Adopting a physics-informed perspective, the toolbox enables the study of spectral and dynamical properties—such as energy gaps and eigenstate structure—that are inaccessible through direct hardware measurements, yet essential for understanding computational hardness and scaling behaviour.

The toolbox successfully computes spectral and dynamical properties for quantum annealing processes derived from data management problems. It reveals energy gaps and eigenstate structures that are critical for understanding computational hardness. For instance, the minimum energy gap $\Delta E_{\min }$ during the annealing schedule is found to correlate with problem difficulty, consistent with the quantum adiabatic theorem. The toolbox also identifies structural similarities between certain database optimisation problems and canonical physical models, such as spin glasses. Visualisation techniques enable the interpretation of optimisation dynamics, showing how the system evolves through the energy landscape. Furthermore, the construction of reduced effective descriptions allows for simplified models that capture the essential physics while being computationally tractable. These results demonstrate the toolbox's capability to provide insights beyond conventional empirical and complexity-theoretic methods.