Topics in Quantum Mechanics

Introduction

In this section, some topics in quantum mechanics will be presented. These are outside the main topic of the book, which is focused on quantum computing and quantum error prevention. Here the topics are of quantum mechanics, but not directly having to do with those main topics of the book.

Time Independent Perturbation Theory

A fairly good introductory treatment of this topic can be found in Griffiths book.

Unitary transformations are represented in a circuit diagram with a box around the unitary transformation. Consider a unitary transformation $V$ on a single qubit state $\left\vert {\psi }\right\rangle$. If the result of the transformation is $\left\vert {\psi ^{\prime }}\right\rangle$, we can then write

	$\left\vert {\psi ^{\prime }}\right\rangle =V\left\vert {\psi }\right\rangle .$	(2.5)

The corresponding circuit diagram is shown in Fig. 2.1.

$\left\vert {\psi }\right\rangle$

$\left\vert {\psi ^{\prime }}\right\rangle$

Figure 2.1: Circuit diagram for a one-qubit gate that implements the unitary transformation $V\,\!$. The input state $\left\vert {\psi }\right\rangle$ is on the left and the output, $\left\vert {\psi ^{\prime }}\right\rangle$, is on the right.