Until now, we have seen qubits only in the braket notation. To get a more visual and geometrical understanding of a single qubit, Arjen will introduce the Bloch Sphere. This three dimensional sphere of radius 1, can also help us understand the action of unitary gates and measurement on a single qubit.

Main Takeaways

• On the Z axis of the Bloch Sphere the eigenstates of the Z basis are found, this also is followed by the X and Y axis.
• The Born Rule is the underlying reason why any single qubit can be represented on the Bloch Sphere.
• Unitary gates operations can be represented as rotations on the Bloch Sphere.
• A measurement on a certain basis projects the qubit state onto one of its eigenstates.