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

10.4 Phase estimation

Let U be an N by N square matrix with complex entries. From section 5.9

det(U − λ IN) = 0
are the eigenvalues1, λ2, …, λN} of U. Some of the λj may be equal. If a particular eigenvalue λ shows up k times among the N, we say λ has multiplicity k.

Each eigenvalue λj corresponds to an eigenvector vj so that

U vj = λj vj
can take each vj to be a unit vector.

When U is unitary, we can say even more: each λj has absolute value 1 and so can be represented as

λj = e2π ϕj i where 0 ≤ ϕj < 1.
This is slightly different notation than we’ve used before, but it is common. It is the product 2π ϕ that is the full radian measure of the rotation.

Now we are ready to pose the question whose solution we outline in this section:

Let U be a quantum transformation...