Section 1
Deutsch's Algorithm
Describe the matrices for the other three functions from $\{0,1\}$ to $\{0,1\}$.
What is the adjoint of the matrix given in Equation (6.9)? Show that this matrix is its own inverse.
Give the unitary matrices that correspond to the other three functions from $\{0,1\}$ to $\{0,1\}$. Show that each of the matrices is its own adjoint and hence all are reversible and unitary.
Using the matrices calculated in Exercise 6.1.3, determine the state $\left|\varphi_2\right\rangle$ for the other three functions.
For each of the other three functions from the set $\{0,1\}$ to the set $\{0,1\}$, describe what $\left|\varphi_2\right\rangle$ would be.
Exercise 6.1.6 For each of the other three functions from the set $\{0,1\}$ to the set $\{0,1\}$, calculate the value of $\left|\varphi_3\right\rangle$.