Chapter 2

Question 1

How does the Z-gate rotate the Bloch sphere?

Answer 1

Rotation about the z-axis by pi.

Question 2

How does the X-gate rotate the Bloch sphere?

Answer 2

Rotation about the x-axis by pi.

Question 3

How does the Y-gate rotate the Bloch sphere?

Answer 3

Rotation about the y-axis by pi.

Question 4

How does the Hadamard rotate the Bloch sphere?

Answer 4

Rotation about the diagonal between the x and z-axis by pi.

Question 5

What is the general parameterisation of unitary rotations around the Bloch sphere?

Answer 5

U = cos(α/2)1 ± in · σ sin(α/2)

Rotation of angle α around the axis defined by the vector n in a clockwise or
anticlockwise direction.