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

8.1 Tensor products

In this section I introduce the linear algebra construction of a tensor product. If the direct sum seems to concatenate two vector spaces, then the tensor product interleaves them. In the first case, if we start with dimensions n and m, we end up with a new vector space of n + m dimensions. For the tensor product, we get n m dimensions.

We can quickly get vector spaces with high dimensions through this multiplicative effect. This means we need to use our algebraic intuition and tools more than our geometric ones.

The initial construction is straight linear algebra but we specialize it to quantum computing and working with multiple qubits in the next section.

Let V and W be two finite dimensional vector spaces over F. Define a new vector space VW, pronounced ‘‘V tensor W’’ or ‘‘the tensor product of V and W,’’ to be the vector space generated by addition and scalar multiplication of...