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

10.1 Quantum Fourier Transform

The Quantum Fourier Transform (QFT) is widely used in quantum computing, notably in Shor’s factorization algorithm in section 10.6 H is the 1-qubit QFT and we’ve seen many examples of its use.

Most treatments of the QFT start by comparing it to the classical Discrete Fourier Transform and then the Fast Fourier Transform. If you don’t know either of these, don’t worry. I’m presenting the QFT in detail for its own sake in quantum computing. Should you know about or read up about the classical analogs, the similarities should be clear.

10.1.1 Roots of unity

We are all familiar with square roots. For example, √4 is equal to either 2 or −2. We can also write √2 = 21/2 and say that there are two ‘‘2nd-roots of 2.’’ Similarly, 5 is a cube root, or ‘‘3rd-root,’’ of 125. In general, we talk about an ‘‘Nth-root’...