Learning Quantum Mechanics through Experience

Huber Nieto–Chaupis

The goal of this paper is the presentation of the elementary procedures that normally are done in nonrelativistic Quantum Mechanics in terms of the principles of Machine Learning. In essence, this paper discusses Mitchell’s criteria, whose block fundamental dictates that the universal evolution of any system is composed by three fundamental steps: (i) Task, (ii) Performance and (iii) Experience. In this paper, the quantum mechanics formalism reflected on the usage of evolution operator and Green’s function are assumed to be part of mechanisms that are inherently engaged to the Machine Learning philosophy. The action for measuring observables through experiments and the intrinsic apparition of statistical or systematic errors are discussed in terms of “quantum learning”.

Devon Bowen

Scott N. Walck

To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The laboratory ideas are naturally expressed in one language, and the theoretical ideas in another. We present a method for learning quantum mechanics that begins with a laboratory language for the description and simulation of simple but essential laboratory experiments, so that students can gain some intuition about the phenomena that a theory of quantum mechanics needs to explain. Then, in parallel with the introduction of the mathematical framework on which quantum mechanics is based, we introduce a calculational language for describing important mathematical objects and operations, allowing students to do calculations in quantum mechanics, including calculations that cannot be done by hand. Finally, we ask students to use the calculational language to implement a simplified version of the laboratory language, bringing together the theoretical and laboratory ideas.

Shan Gao

Huber Nieto–Chaupis

We present a theory of Machine Learning based entirely on the formalism of Quantum Mechanics from the fact that the diverse instances on the application of the algorithms would contain certain concepts linked to stochastic. In this manner, the probabilistic formalism of the Quantum Mechanics might be well applied. Thus, we implement the Mitchell's criteria with mathematical methodologies based on the Hilbert's space as well as the employment of quantum operators to describe the behavior of the experience in terms of probabilities. We illustrate the application of this theory through a quantitative analysis of the time evolution of the experience.

Dennis Dieks