# Notes on: Ekert, A., Hayden, P., & Inamori, H. (2000): Basic concepts in quantum computation

## Table of Contents

## Notation

- stands for where , e.g.

## Definitions

The **Hadamard gate** is a single qubit gate performing the unitary transformation known as the **Hadamard transform** is defined as

or

The **phase shift gate** a single qubit gate defined as:

or in matrix-representation:

The **controlled NOT** gate (`C-NOT`

) flips the second (target) qubit if the first (control) qubit is and does nothing if the control qubit is .

The gate is represented by the unitary matrix

or

and denotes the `XOR`

or addition (or more precisely, *direct sum*) modulo 2.

The **phase shift gate** is a *two-qubit* state defined my

or