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.
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.
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.
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.
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.
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.