A Hands-On Lesson On Quantum Phase Gates

Learn about all the important Phase gates used in Quantum algorithms in this lesson.

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Phase Gates are single-qubit quantum gates that act to change the phase of a qubit’s state without changing its probabilities.

These gates apply a relative phase shift to the qubit’s state.

The general form of a phase gate is represented by the following matrix:

This tells that a phase gate applies a phase e^(iθ) to |1> component of a qubit, while leaving the |0> component unchanged.

The following phase gates are important to know about:

1. Z gate
2. S gate
3. S† gate
4. T gate
5. T† gate

Let’s discuss these in detail.

Z gate

This is the Pauli-Z gate, which we have learned about in the previous lessons.

It is represented by the following symbol in a quantum circuit diagram:

It can be derived from the general phase gate matrix with θ = π :

The Z-gate causes a phase flip for a qubit in the state |1> but leaves |0⟩ unchanged.