Book Image

Essential Mathematics for Quantum Computing

By : Leonard S. Woody III
5 (1)
Book Image

Essential Mathematics for Quantum Computing

5 (1)
By: Leonard S. Woody III

Overview of this book

Quantum computing is an exciting subject that offers hope to solve the world’s most complex problems at a quicker pace. It is being used quite widely in different spheres of technology, including cybersecurity, finance, and many more, but its concepts, such as superposition, are often misunderstood because engineers may not know the math to understand them. This book will teach the requisite math concepts in an intuitive way and connect them to principles in quantum computing. Starting with the most basic of concepts, 2D vectors that are just line segments in space, you'll move on to tackle matrix multiplication using an instinctive method. Linearity is the major theme throughout the book and since quantum mechanics is a linear theory, you'll see how they go hand in hand. As you advance, you'll understand intrinsically what a vector is and how to transform vectors with matrices and operators. You'll also see how complex numbers make their voices heard and understand the probability behind it all. It’s all here, in writing you can understand. This is not a stuffy math book with definitions, axioms, theorems, and so on. This book meets you where you’re at and guides you to where you need to be for quantum computing. Already know some of this stuff? No problem! The book is componentized, so you can learn just the parts you want. And with tons of exercises and their answers, you'll get all the practice you need.
Table of Contents (20 chapters)
1
Section 1: Introduction
4
Section 2: Elementary Linear Algebra
8
Section 3: Adding Complexity
13
Section 4: Appendices
Appendix 1: Bra–ket Notation
Appendix 2: Sigma Notation
Appendix 5: References

Defining matrix multiplication

Matrix multiplication can be a complicated procedure, and we will build up to it gradually. It is defined as an operation between an m × n matrix and an n × p matrix that produces an m × p matrix. The following screenshot shows this well:

Figure 2.4 – Schematic of matrix multiplication

Notice that matrix multiplication is only defined if the number of columns in the first matrix equals the number of rows in the second matrix—or, in other words, the ns have to match in our preceding figure. This is so important that we will give it a special name: the matrix multiplication definition rule, or definition rule for short. Based on this, the first thing you should do when presented with two matrices to multiply is to make sure they pass the definition rule. Otherwise, the operation is undefined. For example, do the following two matrices pass the definition rule?

The answer is no because you have...