# zGate

Pauli Z gate

Since R2023a

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

## Description

example

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

collapse all

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

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

collapse all

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

Example: 1

Example: 3:5

collapse all

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

## Version History

Introduced in R2023a