tGate

T gate

Since R2023a

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

Syntax

g = tGate(targetQubit)

Description

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

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

Applying this gate is equivalent to applying the R1 gate with a rotation angle of π/4, meaning that tGate(targetQubit) is equivalent to r1Gate(targetQubit,pi/4).

Examples

T Gate and Its Matrix Representation

Create a T gate that acts on a single qubit.

g = tGate(1)

g = 

  SimpleGate with properties:

             Type: "t"
    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   0.7071 + 0.7071i

Array of T Gates

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

g = tGate(1:4)

g = 

  4×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   t                1     
     2   t                2     
     3   t                3     
     4   t                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 T Gate

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

$$\left[\begin{array}{cc}1& 0\\ 0& \exp \left(i\frac{\pi }{4}\right)\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& \frac{1+i}{\sqrt{2}}\end{array}\right].$$

Applying this gate is equivalent to applying an R1 gate with a rotation angle of π/4. This gate is also known as the fourth root of Pauli Z gate because applying the T gate four times is equivalent to applying the Pauli Z gate.

Version History

Introduced in R2023a