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

3.4 Rational numbers

The rational numbers, denoted Q, take care of the problem of the integers not being closed under division by non-zero values.

3.4.1 Fractions

Let’s start by talking about fractions, also known as the rational numbers, the way you may have been first introduced to them. This is elementary but useful to review to relate to what we have in the big picture with Q.

Given a loaf of bread, if we cut it right down the middle, we say we have divided it into halves. Fraction-wise, one-half = 1/2. The two halves equal one whole loaf, so 1/2 + 1/2 = 2 × 1/2 = 1. Two halves is 2/2, which is 1. Four halves would make two loaves: 4/2 = 2.

Considering whole loaves, 1/1 is one loaf, 2/1 is two loaves, and 147/1 is one hundred and forty-seven loaves. We can represent any integer n as a fraction inline math.

To multiply fractions, we multiply the tops (numerators) together and put those over the product (the result of multiplication) of the bottoms (denominators...