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inv

Inverse of quantum circuit or gate

Since R2023a

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

Syntax

cinv = inv(c)

Description

example

cinv = inv(c) returns the inverse of a quantum circuit or gate c. The output is another circuit or gate that is the reverse operation of the original circuit or gate. The data type of cinv is the same as the data type of c.

Examples

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Create a quantum circuit that consists of 3 quantum gates.

gates = [hGate(1); sGate(2); rxGate(1,pi/3)];
c = quantumCircuit(gates);

Find the inverse of the quantum circuit. Show the gate operations of the original circuit and the inverted gate operations of the inverse circuit.

cinv = inv(c);
c.Gates

ans = 

  3×1 SimpleGate array with gates:

    Id   Gate   Control   Target   Angle
     1   h                1             
     2   s                2             
     3   rx               1        pi/3 
cinv.Gates

ans = 

  3×1 SimpleGate array with gates:

    Id   Gate   Control   Target   Angle
     1   rx               1        -pi/3
     2   si               2             
     3   h                1

Here, hGate is its own inverse, siGate is the inverse of sGate, and the rotation angle of rxGate has changed sign to rotate backwards.

Construct a y-axis rotation gate with a rotation angle of π/2.

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

  SimpleGate with properties:

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

Find the inverse of the rotation gate.

ginv = inv(g)
ginv = 

  SimpleGate with properties:

             Type: "ry"
    ControlQubits: [1×0 double]
     TargetQubits: 1
           Angles: -1.5708

Construct a composite gate that consists of two inner gates.

gates = [hGate(1); cxGate(1,2)];
cg = compositeGate(gates,[1 2]);

Find the inverse of the composite gate. Show the gate operations of the original composite gate and the inverted gate operations of the inverse composite gate.

cginv = inv(cg);
cg.Gates
ans = 

  2×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   h                1     
     2   cx     1         2
cginv.Gates
ans = 

  2×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   cx     1         2     
     2   h                1

Create a quantum circuit that consists of the composite gate and its inverse. Show that the operations of these gates cancel each other out and the matrix representation of this circuit is an identity matrix.

c = quantumCircuit([cg; cginv]);
M = getMatrix(c)
M =

    1.0000         0         0         0
         0    1.0000         0         0
         0         0    1.0000         0
         0         0         0    1.0000

Input Arguments

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Quantum circuit or gate, specified as a quantumCircuit, SimpleGate, or CompositeGate object.

  • If c is a quantumCircuit or CompositeGate object, then inv reverses the order of the original gates in c and replaces each gate with its inverse.

  • If c is a SimpleGate object, then inv replaces the gate with its inverse.

Version History

Introduced in R2023a

See Also

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