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Imaging Membrane Potential with Two Types of Genetically Encoded Fluorescent Voltage Sensors

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Analogy between Boltzmann Machines and Feynman Path Integrals.

Srinivasan S Iyengar¹, Sabre Kais²

¹Department of Chemistry and Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States.

Journal of Chemical Theory and Computation

|April 26, 2023

Summary

This study reveals mathematical links between Boltzmann machines and Feynman

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Area of Science:

* Computer Science
* Quantum Physics
* Machine Learning

Background:

* Machine learning (ML) significantly impacts various scientific domains.
* Quantum machine learning (QML) is an emerging field for complex problems.
* Foundations of ML face ongoing debate and uncertainty.

Purpose of the Study:

* To explore mathematical connections between Boltzmann machines and quantum mechanics.
* To interpret ML through the lens of Feynman's path integrals.
* To propose quantum circuit models for ML.

Main Methods:

* Mathematical exposition of Boltzmann machines and neural networks.
* Comparison with Feynman's path integral formulation in quantum mechanics.
* Development of general quantum circuit models.

Main Results:

* Boltzmann machines and neural networks share mathematical structures with Feynman paths.
* Hidden layers in ML can be interpreted as discrete path elements.
* ML can be viewed as finding optimal paths and weights, akin to path integrals.

Conclusions:

* Neural networks are intrinsically linked to Feynman path integrals.
* This connection suggests ML as a potential avenue for quantum problems.
* Proposed quantum circuit models bridge Boltzmann machines and path integrals.