xGate

Pauli X gate

Since R2023a

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

Syntax

g = xGate(targetQubit)

Description

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

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

Examples

Pauli X Gate and Its Matrix Representation

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

g = xGate(1)

g = 

  SimpleGate with properties:

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

Get the matrix representation of the gate.

M = getMatrix(g)

M =

     0     1
     1     0

Array of Pauli X Gates

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

g = xGate(1:4)

g = 

  4×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   x                1     
     2   x                2     
     3   x                3     
     4   x                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 X Gate

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

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

This gate maps the $$|0\rangle$$ state to the $$|1\rangle$$ state and maps the $$|1\rangle$$ state to the $$|0\rangle$$ state. This gate is also known as a bit-flip gate and is the quantum equivalent of the classical NOT gate.

Version History

Introduced in R2023a