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These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
This is the first Internet course on elementary quantum mechanics written in Spanish ("castellano") for the benefit of Spanish speaking students. I thank my eight Mexican students at the Institute of Physics, University of Guanajuato, Leon,…
Quantum computing is an emerging paradigm that opens a new era for exponential computational speedup. Still, quantum computers have yet to be ready for commercial use. However, it is essential to train and qualify today the workforce that…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
In this paper, we examine the state art of quantum computing and analyze its potential effects in scientific computing and cybersecurity. Additionally, a non-technical description of the mechanics of the listed form of computing is provided…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
In this series of lectures, we would like to introduce the audience to quantum optimal control. The first lecture will cover basic ideas and principles of optimal control with the goal of demystifying its jargon. The second lecture will…
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…
These are notes from a 15 week course aimed at graduate mathematicians. They provide an essentially self-contained introduction to some of the ideas and terminology of QFT.
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We provide an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
The development of estimation and control theories for quantum systems is a fundamental task for practical quantum technology. This vision article presents a brief introduction to challenging problems and potential opportunities in the…
The concept of time as used in various applications and interpretations of quantum theory is briefly reviewed.
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
This chapter summarizes quantum computation, including the motivation for introducing quantum resources into computation and how quantum computation is done. Finally, this chapter articulates advantages and limitations of quantum…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory,…