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

7.3 The complex math and physics of a single qubit

Let’s revisit our definition of a qubit from section 7.1

Mathematics

A qubit—a quantum bit—is the fundamental unit of quantum information. At any given time, it is in a superposition state represented by a linear combination of vectors |0 and |1 in C2:

a |0 + b |1 where |a|2 + |b|2 = 1 .

Physics

Through measurement, a qubit is forced to collapse irreversibly to either |0 or |1. The probability of its doing either is |a|2 and |b|2, respectively. a and b are called probability amplitudes.

The mathematical portion is linear algebra of a two-dimensional complex vector space. As a vector, the qubit state has length 1. Linear transformations must preserve this length and are isometries. Their matrices are unitary. Being unitary, they are invertible: moving a qubit from...