Book Image

Dancing with Qubits

By : Robert S. Sutor
5 (1)
Book Image

Dancing with Qubits

5 (1)
By: Robert S. Sutor

Overview of this book

Quantum computing is making us change the way we think about computers. Quantum bits, a.k.a. qubits, can make it possible to solve problems that would otherwise be intractable with current computing technology. Dancing with Qubits is a quantum computing textbook that starts with an overview of why quantum computing is so different from classical computing and describes several industry use cases where it can have a major impact. From there it moves on to a fuller description of classical computing and the mathematical underpinnings necessary to understand such concepts as superposition, entanglement, and interference. Next up is circuits and algorithms, both basic and more sophisticated. It then nicely moves on to provide a survey of the physics and engineering ideas behind how quantum computing hardware is built. Finally, the book looks to the future and gives you guidance on understanding how further developments will affect you. Really understanding quantum computing requires a lot of math, and this book doesn't shy away from the necessary math concepts you'll need. Each topic is introduced and explained thoroughly, in clear English with helpful examples.
Table of Contents (16 chapters)
Preface
13
Afterword

5.5 Matrix algebra

So far we have looked at matrices and their relationships to linear maps. We now investigate operations that are relevant when two or more matrices are involved. We cover the general case first of matrices which may have different numbers of rows and columns and then move on to square matrices.

All matrices are over fields in this section and when we are manipulating multiple matrices they all have entries in the same field. We can consider matrices over rings such as the integers but we have no need to make this restriction for quantum computing.

5.5.1 Arithmetic of general matrices

Matrices that are the same size, meaning they have the same number of rows and columns, can be added together entry by entry. For example,

display math
The same is true for subtraction and negation.
display math
Scalar multiplication is done entry by entry.
display math

The set of n by m matrices over a field F for given integers n and m ≥...