Search icon CANCEL
Arrow left icon
Explore Products
Best Sellers
New Releases
Books
Videos
Audiobooks
Learning Hub
Conferences
Free Learning
Arrow right icon
Arrow up icon
GO TO TOP
Dancing with Qubits

You're reading from   Dancing with Qubits How quantum computing works and how it can change the world

Arrow left icon
Product type Paperback
Published in Nov 2019
Publisher Packt
ISBN-13 9781838827366
Length 516 pages
Edition 1st Edition
Arrow right icon
Author (1):
Arrow left icon
Robert S. Sutor Robert S. Sutor
Author Profile Icon Robert S. Sutor
Robert S. Sutor
Arrow right icon
View More author details
Toc

Table of Contents (16) Chapters Close

Preface
1 Why Quantum Computing? FREE CHAPTER 2 They’re Not Old, They’re Classics 3 More Numbers than You Can Imagine 4 Planes and Circles and Spheres, Oh My 5 Dimensions 6 What Do You Mean ‘‘Probably’’? 7 One Qubit 8 Two Qubits, Three 9 Wiring Up the Circuits 10 From Circuits to Algorithms 11 Getting Physical 12 Questions about the Future Afterword
Other Books You May Enjoy Appendices

4.4 From Cartesian to polar coordinates

Each point on the unit circle is uniquely determined by an angle ϕ given in radians such that 0 ≤ ϕ < 2π.

Even though a point on the unit circle is in R2, which is two-dimensional, it takes only one value, ϕ, to determine it. We lost the need for a second value by insisting that the point has distance 1 from the origin.

More generally, let P = (a, b) be a non-zero point (that is, a point which is not the origin) in R2. Let r = √a2 + b2 be the distance from P to the origin. Then the point

Q = (a/r, b/r)
is on the unit circle. There is a unique angle ϕ such that 0 ≤ ϕ < 2π that corresponds to Q. With r we can uniquely identify
P = (r cos(ϕ), r sin(ϕ)) .

tikz JPG figure

(r, ϕ) are called the polar coordinates of P. You may sometimes see the Greek letter ρ (rho) used instead...

lock icon The rest of the chapter is locked
Register for a free Packt account to unlock a world of extra content!
A free Packt account unlocks extra newsletters, articles, discounted offers, and much more. Start advancing your knowledge today.
Unlock this book and the full library FREE for 7 days
Get unlimited access to 7000+ expert-authored eBooks and videos courses covering every tech area you can think of
Renews at €18.99/month. Cancel anytime