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czGate

Controlled Z gate

Since R2023a

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

Syntax

g = czGate(controlQubit,targetQubit)

Description

g = czGate(controlQubit,targetQubit) applies a controlled Z gate to a target qubit based on the state of a control qubit and returns a quantum.gate.SimpleGate object. If the control qubit is in the |0〉 state, then this gate does nothing. If the control qubit is in the |1〉 state, then this gate applies a Pauli Z gate (zGate) to the target qubit.

  • If controlQubit and targetQubit are vectors of the same length, cyGate returns a column vector of gates, where g(i) represents a controlled Z gate applied to a control qubit with index controlQubit(i) and a target qubit with index targetQubit(i).

  • If either controlQubit or targetQubit is a scalar, and the other input is a vector, then MATLAB® expands the scalar to match the size of the vector input.

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

example

Examples

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Create a controlled Z gate that acts on a control qubit with index 1 and a target qubit with index 2.

g = czGate(1,2)
g = 

  SimpleGate with properties:

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

Get the matrix representation of the gate.

M = getMatrix(g)
M =

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0    -1

Create an array of three controlled Z gates. The first gate acts on control qubit 1 and target qubit 2, the next gate acts on control qubit 2 and target qubit 3, and the final gate acts on control qubit 3 and target qubit 4.

g = czGate(1:3,2:4)
g = 

  3×1 SimpleGate array with gates:

    Id   Gate   Control   Target
     1   cz     1         2     
     2   cz     2         3     
     3   cz     3         4

Input Arguments

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

Example: 2

Example: 6:8

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

Example: 1

Example: 3:5

More About

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Matrix Representation of Controlled Z Gate

The matrix representation of a controlled Z gate applied to control qubit 1 and target qubit 2 is

[100001000010000−1].

If the control qubit is in the |0〉 state, then this gate leaves the target qubit as is. If the control qubit is in the |1〉 state, then this gate applies a Pauli Z gate to the target qubit. Because this gate affects only the |11〉 state, swapping the control and target qubits does not change the gate operation.

Version History

Introduced in R2023a

See Also

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