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

4.5 The complex ‘‘plane’’

In the last chapter we discussed the algebraic properties of C, the complex numbers. We return to them again here to look at their geometry. For any point (a, b) in the real plane, consider the corresponding complex number a + bi.

In the graph of the complex numbers, the horizontal axis is the real part of the complex variable z and the vertical axis is the imaginary part. These replace the x and y axes, respectively.

The plot to the right shows several complex values. Despite appearances and some authors’ use of the terminology, that is not a complex plane. A plane has two dimensions. We visualized C, which is one-dimensional, in the two-dimensional real plane. We return to these issues about dimensions with respect to a field in the next chapter when we look at vector spaces.

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Conjugation

Conjugation reflects a complex number across the horizontal Re(z) axis. If the number...