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

4.4 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...