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

3.6 Structure

I took some time to show the operations and the properties of the real numbers and its subsets like the integers and rational numbers because these are very common in other parts of mathematics when properly abstracted. This structure allows us to learn and prove things and then apply them to new mathematical collections as we encounter them. We start with three: groups, rings, and fields.

3.6.1 Groups

Consider a collection of objects which we call G. For example, G might be Z, Q, or R as above. We also have some pairwise operation between elements of G we denote by ‘‘○’’. It’s a placeholder for an action that operates on two objects.

This ‘‘○’’ operation could be addition ‘‘+’’ or multiplication ‘‘×’’ for numbers, but might be something entirely different. Use your intuition with numbers, but understand that the general...