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

8.2 Entanglement

We’ve now seen many gate operations that you can apply to a single qubit to change its state. In section 2.5

While we can apply not to a single bit, all the other operations require at least two bits for input. In the same way, we need to work with multiple qubits to produce interesting and useful results.

8.2.1 Moving from one to two qubits

As discussed above, the states of a single qubit are represented by vectors of length 1 in C2 and all such states that differ only by multiplication by a complex unit are considered equivalent. Each qubit starts by having its own associated copy of C2.

When we have a quantum system with two qubits, we do not consider their collective states in a single C2 instance. Instead, we use the tensor product of the two copies of C2 and the tensor products of the quantum state vectors. This gives us a four-dimensional complex vector space where this ‘‘4’’ is 2 × 2 rather...