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

10.6 Shor’s algorithm

We now have the tools we need to sketch Shor’s algorithm for factoring integers in polynomial time on a sufficiently large quantum computer.

The complete algorithm has both classical and quantum components. Work is done on both kinds of machines to get to the answer. It is the quantum portion that drops us down to polynomial complexity in the number of gates by use of phase estimation, order finding, modular exponentiation, and the Quantum Fourier Transform.

Let odd M in Z be greater than 3 for which you have already tried the basic tricks from subsection 10.2.3 M is not a power of a prime number, and you can use Newton’s method to test this.

So M is an odd positive number in Z that is not a power of a prime. It has a reasonable chance of being composite.

The following is the general approach to Shor’s algorithm given M as above:

  1. Choose a random number a such that 1 < a < M. Keep track of...