Operational Framework for a Quantum Database

Databases are an essential component of modern computing infrastructures and allow efficient manipulation of inherently structured data. The structure depends on the type and relationships of the individual data elements and on the access pattern. Extending the concept of databases to the quantum domain is expected to increase both the storage efficiency and the access parallelism through quantum superposition. In addition, quantum databases may be seen as the result of a prior state preparation ready to be used by quantum algorithms when needed. On the other hand, limiting factors exist and include entanglement creation, the impossibility of perfect copying due to the no-cloning theorem, and the impossibility of coherently erasing a quantum state. In this work, we introduce quantum databases within the broader context of data structures using classical, or more precisely cloneable, and quantum data and indexing. In particular, we are interested in quantum databases' practical implementation and usability, focusing on the definition of the basic operations needed to create and manipulate data stored in a superposition state. Specifically, we address the case of quantum indexing in combination with cloneable data. For this scenario, we define the operations for database preparation, extension, removal of indices, writing, and read-out of data, as well as index permutation. We present their algorithmic implementation and highlight their advantages and limitations. Finally, we introduce the next steps toward defining the same operations in the more general context of quantum indexing and quantum data.