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

3.5 Real numbers

When we’re were done looking at the real numbers we’ll have finished analyzing the typical numbers most people encounter. Let’s begin with decimals.

3.5.1 Decimals

A decimal expression for a real number looks like

  • an optional minus sign,
  • followed a finite number of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9,
  • followed by a period, also called the decimal point,
  • followed by a finite or infinite number of digits.

In many parts of the world, the decimal point is a comma instead of a period, but I use the United States and UK convention here.

If there are no digits after the decimal point then the decimal point may be omitted.

Any trailing 0s on the right are usually omitted when you are using the number in a general mathematical context. They may be kept in situations where they indicate the precision of a measurement or a numeric representation in computer code.

Any leading 0s on the left are usually omitted. We have