Quantum Mechanics and Data-Driven Physics

Mrittunjoy Guha Majumdar

Quantum learning paradigms address the question of how best to harness conceptual elements of quantum mechanics and information processing to improve operability and functionality of a computing system for specific tasks through experience. It is one of the fastest evolving framework, which lies at the intersection of physics, statistics and information processing, and is the next frontier for data sciences, machine learning and artificial intelligence. Progress in quantum learning paradigms is driven by multiple factors: need for more efficient data storage and computational speed, development of novel algorithms as well as structural resonances between specific physical systems and learning architectures. Given the demand for better computation methods for data-intensive processes in areas such as advanced scientific analysis and commerce as well as for facilitating more data-driven decision-making in education, energy, marketing, pharmaceuticals and healthcare, finance and industry.

S. Schramm

Mrittunjoy Guha Majumdar

Quantum learning paradigms address the question of how best to harness conceptual elements of quantum mechanics and information processing to improve operability and functionality of a computing system for specific tasks through experience. It is one of the fastest evolving framework, which lies at the intersection of physics, statistics and information processing, and is the next frontier for data sciences, machine learning and artificial intelligence. Progress in quantum learning paradigms is driven by multiple factors: need for more efficient data storage and computational speed, development of novel algorithms as well as structural resonances between specific physical systems and learning architectures. Given the demand for better computation methods for data-intensive processes in areas such as advanced scientific analysis and commerce as well as for facilitating more data-driven decision-making in education, energy, marketing, pharmaceuticals and healthcare, finance and industry.

Jean‐Michel Gillet

Jean‐Michel Gillet

Stefan Klus, Feliks Nüske, Sebastian Peitz

Abstract Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson’s stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue toward solving Schrödinger’s equation using recently developed tools from data science.