A common problem when learning Quantum Mechanics is the complexity in the mathematical and physical concepts, which leads to difficulty in solving and understanding problems. Using programming languages like Python have become more and more prevalent in solving challenging physical systems. An open-source computer algebra system, SymPy, has been developed using Python to help solve these difficult systems. I have added code to the SymPy library for two different systems, a One-Dimensional Quantum Harmonic Oscillator and a Quantum Mapping Gate used in Quantum Computing.
A common problem when learning Quantum Mechanics is the complexity in the mathematical and physical concepts, which leads to difficulty in solving and understanding problems. Using programming languages like Python have become more and more prevalent in solving challenging physical systems. An open-source computer algebra system, SymPy, has been developed using Python to help solve these difficult systems. I have added code to the SymPy library for two different systems, a One-Dimensional Quantum Harmonic Oscillator and a Quantum Mapping Gate used in Quantum Computing.
Quantum Mechanics can be an abstract and complex subject. Students often complain of confusion, struggle, and frustration as they try to master the topic. The goal of this book is to reduce the complexity and clarify the abstractions with concrete visual examples driven by simple python programs. It is assumed that the reader is concurrently taking a course in quantum mechanics, or self-studying quantum mechanics, but is looking for supplementary material to help with understanding and visualizing how quantum mechanics works. The focus of this book is writing python programs to visualize the underlying behavior of the mathematical theory. The background needed to understand quantum mechanics is differential equations, linear algebra and modern physics. We need a strong foundation in differential equations and linear algebra because the behavior of quantum systems is governed by equations that are written in terms of these concepts. Modern physics includes concepts such as special relativity and quantum phenomena like the photoelectric effect and energy quantization that the theory of quantum mechanics seeks to explain. This book is also not an introduction to the python programming language, or to numpy, or even to VPython. However its programming examples start simply and grow more complex as the chapters progress, so deep expertise in any of these is not a pre-requisite. Key features: · Provides an accessible and practical guide to the abstractions in quantum mechanics with concrete visual examples driven by simple python programs. · Contains few derivations, equations, and proofs. · For complete beginners of python programming, appendix B serves as a very brief introduction to the main concepts needed to understand the code in this book.
This book provides an easy-to-read but practical introduction to quantum gate simulation to serious learners of the subject. Fundamental physical concepts and selected programming examples of quantum simulations are described for readers who want to use the simulation with a physical understanding background without the use of rigorous mathematics. This book is intended to offer a self-study book for senior and graduate students of physics, computer science, and mathematics who want to learn and write quantum codes. It may also serve as a textbook or a reference in academia and industry. Readers are expected to have introductory knowledge of linear algebra although it is briefly reviewed in this book. Some experience of computer programming is helpful, but no prior knowledge of Python is required for writing the quantum codes shown in this book. Part of IOP Series in Quantum Technology. Key features • Easy-to-read content for self-paced readers. • Many examples with background physics. • Detailed description of entanglement and teleportation. • Guide to industrial resources. • DIY quantum gate simulations.
Because aspects of quantum mechanics are both difficult to understand and difficult algebraically, there is a need for software which symbolically simulates quantum me-chanical phenomena. To accomplish this goal, code has been added to an open-source computer algebra system, called SymPy, which models the abstraction of Dirac nota-tion and the density operator. Additionally, a quantum computer simulation has been built using this abstraction. This paper shall discuss the code that has been added as well as any relevant physics important to understanding the code. In particular, we shall focus on the density operator of statistical quantum mechanics using SymPy's density matrices as a guide. 1
This paper discussed the digitization of some analytical solutions of the fundamental equation of non-relativistic quantum mechanics, the Schrödinger equation, in the Python programming environment. The main objective of the work is to automate the solution of several known analytically solvable problems of quantum mechanics and ensure their use in more complex problems. For this purpose, the Python programming environment was chosen, which, due to the large number of libraries and flexibility, is currently widely used in solving physical and mathematical problems. In the program we propose, which is available on the GitHub platform, it is solved easily. The problem of determining the probability of the spatial distribution of an electron in a hydrogen-like atom is discussed. The Schrödinger equation is presented in the spherical coordinate system. The wave function, describing the electron's state, quantized energy values, and probability density, is derived analytically. A recursive function was written in Python to handle the series coefficients defining the wave function. Utilizing relevant libraries, the resulting program constructs electron spatial distribution functions for different excitation levels. The paper then examines two one-dimensional tunneling scenarios and provides the tunneling coefficients in analytical form. A Python program was developed to plot the dependence of these coefficients on the particle's coordinate and energy. All the code is available on GitHub.
Q UANTUM MECHANICS can be an abstract and complex subject. Students often complain of confusion, struggle, and frustration as they try to master the topic. The goal of this book is to reduce the complexity and clarify the abstractions with concrete visual examples driven by simple python programs. It is assumed that the reader is concurrently taking a course in quantum mechanics, or self-studying quantum mechanics, but is looking for supplementary material to help with understanding and visualizing how quantum mechanics works. There are few derivations, equations, or proofs. Those are left to the more formal textbooks and lectures. The focus of this book is writing python programs to visualize the underlying behavior of the mathematical theory. The background needed to understand quantum mechanics is differential equations, linear algebra and modern physics. We need a strong foundation in differential equations and linear algebra because the behavior of quantum systems is governed by equations that are written in terms of these concepts. Modern physics includes concepts such as special relativity and quantum phenomena like the photoelectric effect and energy quantization that the theory of quantum mechanics seeks to explain. This book is also not an introduction to the python programming language, or to numpy, or even to VPython. Having said that, the programming examples will start simply and grow more complex as the story line progresses, so deep expertise in any of these is not a pre-requisite. If you're completely new to python programming, appendix B has been provided as a very brief introduction to the main concepts needed to understand the code in this book.
In this chapter you will get started with the QISKit, the best SDK out there for quantum programming. You will learn how easy it is to install the SDK in your local system. But before writing your first quantum program, it is always helpful to understand what quantum computation is and how it differs from classical computation. For this purpose, a very basic explanation of qubit states and quantum gates is presented using linear algebra. This section also shows how quantum computation can mirror its classical counterpart and furthermore find shortcuts to get results faster. Next, the chapter walks through the anatomy of a quantum program including system calls, circuit compilation formats, quantum assembly, and more.