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

5.2 Vector spaces

The last section introduced several ideas about vector spaces using familiar notions from R2 and C. It’s time to generalize.

Let F be a field, for example R or C, and let V be a set of objects. These objects are called vectors and are shown in bold such as v. We are interested in defining a special kind of multiplication, called scalar multiplication, and addition.

If s is in F then we insist sv is in V for all v in V. This means the set V is closed under multiplication by scalars from the field F. While V may have some kind of multiplication defined between its elements, we do not need to consider it here.

For any v1 and v2 in V, we also insist v1 + v2 is in V and that the addition is commutative. Thus V is closed under addition. In fact, we demand V has an element O and additive inverses so that V is a commutative additive group.

V is almost a vector space over F but we have to insist on a few more conditions related to scalar multiplication...