# Synchronous Interactions Between Quantum and Macroscopic Systems

This project calculates synchronous quantum systems and macroscopic systems with well-defined interactions. I would like information about any other similar projects that might guide this one.

This project was mapped out in several publications, recently in

L. Ingber, ``Quantum calcium-ion interactions with EEG,'' Sci 1 (7), 1-21 (2018). [ URL https://www.ingber.com/smni18_quantumCaEEG.pdf and https://doi.org/10.3390/sci1010020 ]

which was performed with the help of XSEDE.org supercomputer resources from Feb 2013 through Dec 2018. The Abstract is given below, and that Conclusion is the starting point of this project.

This project would use quantum computing in one or both contexts:

(a) to perform the optimization of the cost/objective function over the space of parameters defined by the SMNI model with EEG data as input.

(b) to propagate the Ca2+ wave function between EEG epochs in lock-step with the changing magnetic vector potential defined by highly synchronous neuronal firings.

Background:

Previous papers have developed a statistical mechanics of neocortical interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated Annealing (ASA) has been developed to perform fits to such nonlinear stochastic systems. An N-dimensional path-integral algorithm for quantum systems, qPATHINT, has been developed from classical PATHINT. Both fold short-time propagators (distributions or wave functions) over long times. Previous papers applied qPATHINT to two systems, in neocortical interactions and financial options.

Objective:

In this paper the quantum path-integral for Calcium ions is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales. Using fits of this SMNI model to EEG data, including these effects, will help determine if this is a reasonable approach.

Method:

Methods of mathematical-physics for optimization and for path integrals in classical and quantum spaces are used for this project. Studies using supercomputer resources tested various dimensions for their scaling limits. In this paper the quantum path-integral is used to derive a closed-form analytic solution at arbitrary time that is used to calculate interactions with classical-physics SMNI interactions among scales.

Results:

The mathematical-physics and computer parts of the study are successful, in that there is modest improvement of cost/objective functions used to fit EEG data using these models.

Conclusion:

This project points to directions for more detailed calculations using more EEG data and qPATHINT at each time slice to propagate quantum calcium waves, synchronized with PATHINT propagation of classical SMNI.

Thanks.

Lester Ingber

## Comments

Murray T(Report)I think this would be new work in the field. I don't think I've seen previous projects using the same techniques.

It looks like you're using a neural network model for your analysis. Can you map a model of these systems to an undirected neural network with discrete activation events of a BQM form?

https://support.dwavesys.com/hc/en-us/community/posts/360017439853-Difference-between-BQM-Ising-and-QUBO-problems-

Are you looking for the Boltzmann distribution over this undirected neural network model? Or are you planning to fit that kind of model to the physical model you're studying?

Lester I(Report)Murray:

Hi. Thanks for your reply.

No, I'm not using any neural nets.

For the classical system, I have a well-developed multivariate multiplicative (e.g., nonlinear in all variables) time-dependent distribution that is analytic for the short-time propagator which has been developed in some publications with my path-integral code PATHINT. This has been fit previously to several sources of EEG data gathered from subjects during short-term memory tasks, associated with highly synchronous neural firings. These firings also give rise to a magnetic vector potential. I have derived this propagator in multiple publications.

For the quantum system, I have derived a closed form wave-function of Ca2+ free ion-packets that are generated by tri-synaptic neuron-astrocyte-neuron interactions, which also contains this external vector potential above. The fairly continuous interactions of this wave-packet with new and leaving Ca2+ ions presents a possible Zeno process that might prolong the life of the wave packet for 100's of ms. The derivation of this wave-function has been derived in multiple publications. I have published some calcs showing the propagation of this wave-function using my qPATHINT code.

Thus, the classical and quantum systems may interact and thereby influence each other. iI have included this interaction in fits to EEG data with modest improvements in the overall cost function. However, a true classical-quantum simulation (using classical computation in sync with quantum calculations) may shed some light on the existence or limitation of these interactions.

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