A set theoretical approach to organise data, based on predicate logic, has been proposed by Ted Codd at IBM. The relational model was derived, followed by normalisation procedures. Discovering complex relationships among data by means of database technology helped growth in businesses, spanning from the largest to the smallest.

In this article, we reflect on a scale-space approach to modelling data suitable for quantum computing and analysis. Topological maps of coupled data sets have been applied in various disciplines, mathematically described by the quantum information theory of stochastic resonance synergies1. This scale-space approach organises data in an atomic structure of binding synergies.

Relational data structure of binding synergies (information)

We have derived the method based on an analogy to the physical computation of signal distortion. The quantum fields encode transition symmetries of synergistically coupled clusters of information in Lagrangian dynamics. Dynamical cascade diagrams are computed from the partition function decomposition. This multiscale approach has been applied in multidimensional data mining and knowledge discovery. The scale invariances have been assessed for various data sets. We have analysed a high dimensional set of proteins2. An approach to attention, memory, and behavioural data-driven study has been proposed3.

This quantum computing approach applies the principle of least action, as described in our reports. The essential part of implementing the least action while preserving the information transfer is by the scale-space tunnelling, introduced in our work4. The scale-space waves propagate information conforming with the mass (information) conservation principle. The bipartite data distributions exchange information synergistically, resonating up-and down-scale waves in dynamical equilibrium.

The scale-space approach

The information applied by two operators, rotor and divergence, acting on the scale-space wave, propagates across the scales. The multiscale decomposition of a partition function binds the minimal circular paths of the information flow in an atomic structure. A quadrupole information carrier encodes the binding structure of a circular data pattern.

Data clusters arranged by binding synergies of the quadrupoles in an atomic structure derive a modelling approach to data mining analysis tool.

Up-scale data join

Join operation fuses data structures of the atoms chosen. This operation results in an increase of the scale parameter β and the entropy of data.

Down-scale data select

The subsystem of the atoms chosen in a data join is decomposed to a lower entropy state by the scale-space wave information propagation that satisfies the information conservation principle. Select operation takes a quadrupole's relational structure in querying information about the arrangement of data. The whole set of quadrupoles and the binding synergies of an atom encapsulates the information queried from a data join.

We envision extended applications of such a database analysis tool in different disciplines, from material and life sciences to financial markets modelling.

Concluding remarks

In this article, we have proposed a quantum computing approach to relational database analysis and knowledge discovery. This approach is based on the theory of stochastic resonances, encapsulating data with binding synergies in an atomic structure. High dimensional data sets are organised in topological maps at multiple scales of decomposition. We have reflected on querying binding synergies (information) of its relational database structure.

References

1 Jovovic, M., Stochastic Resonance Synergetics. Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015.
2 Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
3 Jovovic M., Attention, Memories and Behavioural Data-driven Study, Advances in Neurology and Neuroscience, 2019.
4 Jovovic, M., Hierarchical scale quantization and coding of motion information in image sequences, Informacione Tehnologije VI, Zabljak, 2002.