Numerical Recipes in Quantum Information Theory and Quantum Computing

An Adventure in FORTRAN 90

M.S. Ramkarthik, Payal D. Solanki

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367759285
• eBook ISBN: 9781000423808
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This first of a kind textbook provides computational tools in Fortran 90 that are fundamental to quantum information, quantum computing, linear algebra and one dimensional spin half condensed matter systems. Over 160 subroutines are included, and the numerical recipes are aided by detailed flowcharts. Suitable for beginner and advanced readers alike, students and researchers will find this textbook to be a helpful guide and a compendium.

Key Features:

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• Includes 160 subroutines all of which can be used either as a standalone program or integrated with any other main program without any issues.

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• Every parameter in the input, output and execution has been provided while keeping both beginner and advanced users in mind.

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• The output of every program is explained thoroughly with detailed examples.

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• A detailed dependency chart is provided for every recipe.

1

Introduction to FORTRAN 90

For those who are new to the FORTRAN [1, 2, 3] programming language this chapter will give a detailed explanation of the FORTRAN 90 language, its syntax and structure. In this chapter we give a brief introduction to the FORTRAN 90 programming language. This we feel is important because it can provide a ready reference for those who use this book. FORTRAN is an open source distribution wherein anyone is free to download and use it. FORTRAN was developed by John Backus and his team at IBM [4] in 1957 specifically designed for scientific programming. In fact, the name FORTRAN stands for FORmula TRANslation and the FORTRAN code is more mathematically readable. From then on, the language has evolved exponentially with various features being updated in every release of it. The modern version of FORTRAN has many new features in it. However, we will be adhering to FORTRAN 90 throughout this book.

In the further sections we will give a complete view of FORTRAN 90. The program is written in any of the infinite text editors available in the web market and this program file should have file extension as ‘.f90' for the compiler to recognize it. All the programs in FORTRAN start with the keyword PROGRAM and it ends with END PROGRAM. FORTRAN uses ‘implicit real(a - h, o - z)' reserves i to n as an integer by default and the complementary alphabets as real. However, if we use ‘implicit none', it allows us to define a variable of our choice. The authors feel that implicit none is better as we will have control over our variables declared and it will facilitate easy debugging, however this is purely the choice of the programmer. FORTRAN codes are case insensitive except for string literals. Also note that FORTRAN handles single and double precision with equal ease. The single precisi...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• List of Figures
• Acknowledgment
• 1 Introduction to FORTRAN 90
• 2 Nuts and Bolts of Quantum Mathematics
• 3 Numerical Linear Algebra and Matrix Operations
• 4 Tools of Quantum Information Theory
• 5 Quantum Entanglement and Its Quantification
• 6 One-Dimensional Spin Chain Models in Condensed Matter Theory
• 7 Random Matrices and Random Vectors
• Dependency Chart
• Bibliography
• Subject Index