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

4.3 Trigonometry

Trigonometry is the study of triangles, angles, and length. The Greek word trig¯onon means ‘‘triangle’’ and metron means ‘‘measure.’’ For the most part we restrict ourselves to triangles with hypotenuse equal to 1, and so within the unit circle.

4.3.1 The fundamental functions

Many people have heard that a circle has 360 degrees, also written 360°. Why 360? If you look around the web you’ll find stories about ancient Mesopotamians, Egyptians, and base 60 number systems. Whatever the reason, 360 is a great number because it is divisible by so many other numbers like 2, 3, 4, 5, 6, 8, 10, 12, 15, and so on. That is, it’s easy to work with portions of 360° that are nice round whole numbers.

Degrees don’t really have a natural meaning in mathematics though. They are simply a convenient unit of measurement. Instead, we use radians.

A circle of radius r has circumference...