Multidimensional information scaling in 5-dimensional quantas has been studied. Quantum information electromagnetism has been proposed for describing the dynamics of multidimensional system scaling.

In this article, I reflect on my career endeavor in modeling stochastic resonance synergies on classical computers. We discuss the advantages and prospects of applying quantum computing to the analysis of large scale complex systems.

### Can we compute stochastic resonances on classical computers?

Various complex system simulations have been performed on classical computers and described in our reports. In our approach, computing is carried out by coupled oscillators. This solves the problem of "negative probabilities" that occur in some other approaches. It explains reversibility in information flows and also shows a way of describing "dark" vs. "light" energy and matter. Stochastic resonance binds information carriers, "light" or "dark." A holographic principle for expressing the circular composition of the information carriers has been proposed.

When I started working on wave information propagation in large spaces, I had the fastest workstation on my office desk. It took me nonetheless, after nights of running simulations of the mathematical description, to check how it translates in numerics with test signal decompositions. It has been 30 years since then. With a small data size and dimensions, I get those results with a touch on my laptop now.

### Personal career endeavor

Arguably, one could envision linear partial differential equations and their solutions. From my experience, however, non-linear transformations of signals in multiple dimensions appear quite difficult. Much more is needed to fully understand the evolving processes of signal transformation. Without help from computer simulations it would be a daunting task, in my opinion.

Synergistic coordinate transformations in a coupled information exchange have been studied in 5-dimensional scale-spaces. The calculus of path integration of stochastic resonance synergies has been derived. The scale-space waves propagate information along multiple dimensions and scales.

The numerical implementation of the scale-space wave equation includes two sequentially alternating iterations:

• Multidimensional data decomposition into two principal components and,
• Synergistic information exchange of two coupled data decompositions via quantum tunneling. It has been applied, however, in our work without a general proof of convergence in 5-dimensional scale-spaces.

Instead, we have studied the asymptotic freedom of motion in the synergistic dynamics of data triplets. The green function of the scale-space quantum fields has been derived. Algebraically, this function preserves information about prime number structure decomposition. The invariance of prime number structure distribution, in triplets, translates to the so-called fine structure constant in theoretical physics.

Stochastic resonance synergies inherit different properties of quantum information electromagnetism depending on how they are derived in a scale cascade of binding synergies. The inheritance framework of quantum descriptors shows a new way to look at the group periodic arrangements of atomic compositions.

### In the prospect of quantum computing

Multidimensional information scaling and the scale-space topology have been proposed for the analysis of large data sets. Computing stochastic resonances in 5-dimensional quantas makes it a steady tool in the application process.

With the advantage of speed and topological pattern expression, mapping a quantum information theory on quantum computers would help improve our understanding of the actual dynamical processes involved in a complex system analysis. Thus opening new avenues in large multidimensional data research. From physicists to biology, possibly in social sciences and economics, too.

### Concluding remarks

In this article, I have reflected on our 30 years of developing the quantum information theory of stochastic resonance synergies. Common lines in our research describe coupled wave information propagation, binding, and expression of quantum information in 5-dimensional scale spaces.

Quantum field dynamics have been described in our reports. The mathematical description has been translated numerically and studied with simulations on classical computers. The prospects of complex systems research and the application of quantum computers have been discussed.

#### 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., Quantum information electromagnetism, Meer Magazine, October 5, 2023.
3 Jovovic. M. The Light and Sound Triplet Codes in Human Perception -- Making Sense of the World in 5D, Acta Scientific Neurology 6.7: 22-23. 2023.
4 Jovovic, M. Quantum fields adaptive signal processing and communication in multiple of scales, 2022.
5 Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
6 Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003.
7 Jovovic, M., Image segmentation for feature selection from motion and photometric information by clustering, SPIE Symposium on Visual Information Processing V, Orlando, 1996.