No man ever steps in the same river twice. For it’s not the same river and he’s not the same man.

(Heraclitus)

Research and study of a large variety of networked complex systems increasingly relies on quantum computing. From quantum physics and biology to cosmology. Quantum information theories and quantum tunnelling play a central role in the quantum computing technologies.

Stochastic resonance synergetic theory, as described in our reports, is an approach to the networked systems dynamics and computation. We have proposed it with methodologies for data analysis in computational physics, neuroimaging, attention, memory, and behavioural data-driven studies.

Network is "everything"

A multidimensional scaling property of the atomic structure has been derived as a dynamical structure within the theory of stochastic resonances. This makes it a bridge to the mathematical foundation of a quantum field theory, in our view2-4. A polynomial distribution limits the asymptotic freedom of information exchange.

The quantum field equation encodes dynamics and symmetries of synergistically coupled clusters of information. Double spaced clusters exchange information by the scale-space wave information propagation and quantum tunneling. Covariance differentiability of a Lagrangian is applied along 2 principal components, with the coordinates transforming dynamically, with β. At the state of scale resonance, two coupled oscillators encode a 5D descriptor of the quantum information carrier.

Packets of multidimensional information obey an uncertainty relation that varies in scale. Its formulation in 2D coordinate frames is given in our reports, as well.

This quantum computing approach applies the principle of least action, as described in our reports. The expression of the exploration of a configuration space is given by its path integral.

"Everything" and "nothing" relate to each other

Black hole singularities have been predicted from the General Theory of Relativity. The way they interact with surrounding galaxies and larger structures, code and exchange information, has been an active research area in cosmology since then.

In our theoretical description, the scale dimension limits asymptotic freedom of movement, at β = 0. Decomposition of the partition function is singular in scale at both ends of a conjoined space - at the infinitely large and at the smallest state of no geometry, the point-like features.

It describes the connection between the largest and the smallest structures in a coupled network. Its relativistic space-time domain description derives from the network of synergistically coupled oscillators.

"Everything" may not be a network

The existence and role of free will is a long-time debated topic amongst philosophers and scientists. "To be, or not to be?", famously quoted from Shakespeare. Every decision one makes, the action taken changes the environment of our existence.

In a world of conserved properties, such a statement, expressed in a language of mathematics, opens the door to a multiverse interpretation of reality. Subsiding the uniqueness of the "Big Bang" origin of the Universe. Rather, one of many events resulting from quantum fluctuations, in this interpretation.

It is not the strongest of the species that survives, nor the most intelligent that survives. It is the one that is the most adaptable to change.

(Charles Darwin)

References

Jovovic, M., Hierarchical scale quantization and coding of motion information in image sequences, Informacione Tehnologije VI, Zabljak, 2002.
Jovovic, M., H. Yahia, and I. Herlin, Hierarchical scale decomposition of images – singular features analysis, INRIA, 2003.
Jovovic, M., and G. Fox, Multi-dimensional data scaling – dynamical cascade approach, Indiana University, 2007.
Jovovic, M., Stochastic Resonance Synergetics – Quantum Information Theory for Multidimensional Scaling, Journal of Quantum Information Science, 5/2:47-57, 2015.
Jovovic M. Attention, Memories and Behavioral Data-driven Study, Advances in Neurology and Neuroscience, 2019.