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

3.1 Natural numbers

While there are special and famous numbers like π, the numbers we use for counting are much simpler: 1, 2, 3, …. I might say ‘‘Look, there is 1 puppy, 2 kittens, 3 cars, and 4 apples.’’ If you give me 2 more apples, I will have 6. If I give my sister 1 of them, I will have 5. If I buy 2 more bags of 5 apples, I will have 15 in total, which is 3 × 5.’’ The set of natural numbers is the collection of increasing values

{1, 2, 3, 4, 5, 6, 7, …}
where we get from one number to the next by adding 1. 0 is not included. The braces ‘‘{‘‘ and ‘‘}’’ indicate we are talking about the entire set of these numbers.

When we want to refer to some arbitrary natural number but not any one specifically, we use a variable name like n and m.

The set of natural numbers is infinite. Suppose otherwise and that some specific number n...