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Dancing with Qubits - Second Edition

You're reading from  Dancing with Qubits - Second Edition

Product type Book
Published in Mar 2024
Publisher Packt
ISBN-13 9781837636754
Pages 684 pages
Edition 2nd Edition
Languages
Author (1):
Robert S. Sutor Robert S. Sutor
Profile icon Robert S. Sutor

Table of Contents (26) Chapters

Preface I Foundations
Why Quantum Computing They’re Not Old, They’re Classics More Numbers Than You Can Imagine Planes and Circles and Spheres, Oh My Dimensions 6 What Do You Mean “Probably”? II Quantum Computing
One Qubit Two Qubits, Three Wiring Up the Circuits From Circuits to Algorithms Getting Physical III Advanced Topics
Considering NISQ Algorithms Introduction to Quantum Machine Learning Questions about the Future Afterword
A Quick Reference B Notices C Production Notes Other Books You May Enjoy
References
Index
Appendices

4.2 The real plane

When we were building up the structure of the integers, we showed the traditional number line R2.

Displayed math

with the negative integers to the left of 0 and the positive ones to the right. Really, though, this was just part of the real number line:

Displayed math

The line is one-dimensional in that we need only one value, or coordinate, to locate a point uniquely on the line. For a real number x, we represent the point on the line by (x). For example, the point (–2.6) is between the markings –3 and –2. We use or omit the parentheses when it is clear from the context whether we are referring to the point or the number that gives its relative position from 0.

Displayed math

I drop the decimal points on the labels now that it is clear we have real numbers.

4.2.1 Moving to two dimensions

Suppose the number line sits in two dimensions so that we extend upwards and downwards:

Displayed math

Since we...

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