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rxxGate

Ising XX coupling gate

Since R2023a

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

Description

g = rxxGate(targetQubit1,targetQubit2,theta) applies an Ising XX coupling gate to two target qubits with a phase parameter theta and returns a quantum.gate.SimpleGate object.

  • If targetQubit1, targetQubit2, and theta are vectors of the same length, rxxGate returns a column vector of gates, where g(i) represents an Ising XX coupling gate applied to the ith element triplet of targetQubit1, targetQubit2, and theta.

  • If any of targetQubit1, targetQubit2, or theta is a scalar, and at least one of the inputs is a vector, then MATLAB® expands the scalar to match the size of the vector input.

  • The qubit indices in each element pair of targetQubit1 and targetQubit2 must not be the same.

example

Examples

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Create an Ising XX coupling gate that acts on two target qubits with indices 1 and 2 using a phase parameter of pi/2.

g = rxxGate(1,2,pi/2)
g = 

  SimpleGate with properties:

             Type: "rxx"
    ControlQubits: [1×0 double]
     TargetQubits: [1 2]
           Angles: 1.5708

Get the matrix representation of the gate.

M = getMatrix(g)
M =

   0.7071 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 - 0.7071i
   0.0000 + 0.0000i   0.7071 + 0.0000i   0.0000 - 0.7071i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 - 0.7071i   0.7071 + 0.0000i   0.0000 + 0.0000i
   0.0000 - 0.7071i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.7071 + 0.0000i

Create an array of three Ising XX coupling gates. The first gate acts on target qubits 1 and 2 with phase parameter pi/4, the next gate acts on target qubits 2 and 3 with phase parameter pi/2, and the final gate acts on target qubits 3 and 4 with phase parameter 3*pi/4.

g = rxxGate(1:3,2:4,pi/4*(1:3))
g = 

  3×1 SimpleGate array with gates:

    Id   Gate   Control   Target   Angle
     1   rxx              [1,2]    pi/4 
     2   rxx              [2,3]    pi/2 
     3   rxx              [3,4]    3pi/4

Input Arguments

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

Example: 1

Example: 3:5

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

Example: 2

Example: 6:8

Phase parameter, specified as a real scalar or vector.

Example: pi

Example: (1:3)*pi/2

More About

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Matrix Representation of Ising XX Coupling Gate

The matrix representation of an Ising XX coupling gate applied to two target qubits with a phase parameter of θ is

exp(iθ2XX)=exp(iθ2[0110][0110])=[cos(θ2)00isin(θ2)0cos(θ2)isin(θ2)00isin(θ2)cos(θ2)0isin(θ2)00cos(θ2)].

Version History

Introduced in R2023a