Archives for July, 2024
Feynman’s Quantum Computer
Feynman's Quantum Computer Richard Feynman was one of the pioneers in the field of quantum computation. His work laid the groundwork for understanding how quantum systems could be used to…
Reversibility versus Irreversibility in Quantum Computation
Reversibility versus Irreversibility in Quantum Computation - Feynman Reversibility is a fundamental concept in quantum computing, contrasting with classical computing, where operations are often irreversible. Reversibility: Quantum computations are inherently…
Feynman’s paths and bohm’s paths in quantum theory
A recap of the Article - Bohm and Feynman Path Integrals - author - Marius Oltean, U Waterloo. Feynman's Path Integral Feynman's approach to quantum mechanics involves the concept of…
Information and Coding Theory
Concepts of Information: Information is defined in terms of probability and surprise. The less likely a message is, the more information it carries. Shannon's definition of information as the base-two…
The Halting Problem for Turing Machines
The Halting Problem for Turing Machines The Halting Problem is a fundamental concept in the theory of computation, specifically related to Turing machines. A Turing machine is a mathematical model…
Quantum vs. Classical States of a Combined System
A classical state doesn't require basis vectors - since it is a simple POINT in phase space. This is true even of combined states in classical physics. In QM, every…
Minkowski and Lorentz Transformations
Minkowski proposed that time itself should be considered as one of the coordinate axes, alongside the three spatial dimensions Lorentz Transformation: The concept of Lorentz transformations, which describe how…
Galois group of a polynomial
The Galois group of a polynomial is a concept in the field of algebra, specifically within Galois theory, which studies the relationship between field extensions and group theory. The Galois…
Boltzmann Entropy and Information Entropy
Boltzmann Entropy Overview Boltzmann entropy is a concept from statistical mechanics, introduced by the Austrian physicist Ludwig Boltzmann. It provides a statistical description of the thermodynamic entropy of a system.…
The Galois Group and Representation Theory
Galois Group Overview The Galois group is a concept from the field of algebra, specifically in the study of field theory and polynomial equations. It is named after the French…