sGate

S gate

Since R2023a

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

Syntax

g = sGate(targetQubit)

Description

g = sGate(targetQubit) applies an S gate to a single target qubit and returns a quantum.gate.SimpleGate object.

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

Applying this gate is equivalent to applying an R1 gate with a rotation angle of π/2, meaning that sGate(targetQubit) is equivalent to r1Gate(targetQubit,pi/2).

Examples

S Gate and Its Matrix Representation

Create an S gate that acts on a single qubit.

g = sGate(1)

g = 

  SimpleGate with properties:

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

Get the matrix representation of the gate.

M = getMatrix(g)

M =

   1.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 1.0000i

Array of S Gates

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

g = sGate(1:4)

g = 

  4×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   s                1     
     2   s                2     
     3   s                3     
     4   s                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 S Gate

The matrix representation of an S gate applied to a single qubit is

$$\left[\begin{array}{cc}1& 0\\ 0& \exp \left(i\frac{\pi }{2}\right)\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& i\end{array}\right].$$

Applying this gate is equivalent to applying an R1 gate with a rotation angle of π/2. This gate is also known as the square root of Pauli Z gate because applying the S gate twice is equivalent to applying the Pauli Z gate.

Version History

Introduced in R2023a