zGate

Pauli Z gate

Since R2023a

Installation Required: This functionality requires MATLAB Support Package for Quantum Computing.

Syntax

g = zGate(targetQubit)

Description

g = zGate(targetQubit) applies a Pauli Z gate to a single target qubit and returns a quantum.gate.SimpleGate object.

If targetQubit is a vector of qubit indices, zGate returns a column vector of gates, where g(i) represents a Pauli Z gate applied to a qubit with index targetQubit(i).

Examples

Pauli Z Gate and Its Matrix Representation

Create a Pauli Z gate that acts on a single qubit.

g = zGate(1)

g = 

  SimpleGate with properties:

             Type: "z"
    ControlQubits: [1×0 double]
     TargetQubits: 1
           Angles: [1×0 double]

Get the matrix representation of the gate.

M = getMatrix(g)

M =

     1     0
     0    -1

Array of Pauli Z Gates

Create an array of Pauli Z gates that act on qubits with indices 1 to 4.

g = zGate(1:4)

g = 

  4×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   z                1     
     2   z                2     
     3   z                3     
     4   z                4     

Input Arguments

targetQubit — Target qubit of gate

positive integer scalar | positive integer vector

Target qubit of the gate, specified as a positive integer scalar index or vector of qubit indices.

Example: 1

Example: 3:5

More About

Matrix Representation of Pauli Z Gate

The matrix representation of a Pauli Z gate applied to a single qubit is

$$\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right].$$

This gate leaves the $$|0\rangle$$ state as is and maps the $$|1\rangle$$ state to $$-|1\rangle$$. This gate is also known as a phase-flip gate.

Version History

Introduced in R2023a