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

5.1 R2 and C1

We looked earlier at the real plane as a set of standard Cartesian coordinate pairs (x, y) with x and y in R representing points we can plot. Now we give these pairs an algebraic structure so that if u and v are in R2 then so is u + v. Also, if r is in R, then rv is in R2 as well. We carry out the addition coordinate by coordinate. The multiplication by r, called scalar multiplication, is also done that way.

If u = (u1, u2) and v = (v1, v2),

u + v = (u1 + v1, u2+v2)
ru = (ru1, ru2)

Using the origin O = (0, 0) as the identity element, R2 is a commutative group under addition. R2 is a two-dimensional vector space over R. This is possible because R is a field.

Rather than considering them as pairs or points, we now call u and v vectors. I use bold to indicate a variable or a ‘‘point’...