Until now, we have seen qubits only in the braket notation. To get a more visual and geometrical understanding of a single qubit, Arjen Vaartjes (QuTech) 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.
- Bra-ket notation
- Basic linear algebra
Knowing that the bit flip gate X takes |0> to |1>, which of the below could be a valid matrix representation for the bit flip gate?
Given that H (the Hadamard gate) acting on |0> produces |+>, i.e. H|0>=|+>, and that H|1> = |->, which of the following could be a valid matrix representation for the Hadamard gate?
For a more visual information on the Bloch sphere see https://youtu.be/0BYWoxM1kVU.