hGate

Hadamard gate

Since R2023a

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

Syntax

g = hGate(targetQubit)

Description

g = hGate(targetQubit) applies a Hadamard gate to a single target qubit and returns a quantum.gate.SimpleGate object.

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

Examples

Hadamard Gate and Its Matrix Representation

Create a Hadamard gate that acts on a single qubit.

g = hGate(1)

g = 

  SimpleGate with properties:

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

Get the matrix representation of the gate.

M = getMatrix(g)

M =

    0.7071    0.7071
    0.7071   -0.7071

Array of Hadamard Gates

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

g = hGate(1:4)

g = 

  4×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   h                1     
     2   h                2     
     3   h                3     
     4   h                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 Hadamard Gate

The matrix representation of a Hadamard gate applied to a single qubit is

$$\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right].$$

This gate maps the qubit basis states from the Z basis to the X basis (and from the X basis to the Z basis), where the $$|0\rangle$$ and $$|1\rangle$$ states are mapped to the $$|+\rangle =\frac{|0\rangle +|1\rangle }{\sqrt{2}}$$ and $$|-\rangle =\frac{|0\rangle -|1\rangle }{\sqrt{2}}$$ states, respectively.

Version History

Introduced in R2023a