Pauli
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Pauli | |
Produces a Pauli operator | |
Other toolboxes required | none |
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Related functions | GellMann GenGellMann GenPauli PauliChannel |
Function category | Special states, vectors, and operators |
Pauli is a function that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:
\[X = \begin{bmatrix}0 & 1\\ 1 & 0\end{bmatrix}, \ \ Y = \begin{bmatrix}0 & -i\\ i & 0\end{bmatrix}, \ \ Z = \begin{bmatrix}1 & 0\\ 0 & -1\end{bmatrix}, \ \ I = \begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}.\]
This function can also produce multi-qubit Pauli operators.
Syntax
- P = Pauli(IND)
- P = Pauli(IND,SP)
Argument descriptions
- IND: An index indicating which Pauli operator you would like to be generated. Values of 1, 2, 3, and 0 correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of 'I', 'X', 'Y', and 'Z' are also accepted, and indicate the Pauli identity, X, Y, and Z operators, respectively. If IND is a vector then this function returns a multi-qubit Pauli operator whose action on the K-th qubit is the same as Pauli(IND(K)).
- SP (optional, default 1): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.
Examples
Single-qubit examples
>> full(Pauli('X'))
ans =
0 1
1 0
>> full(Pauli(1))
ans =
0 1
1 0
>> full(Pauli(0))
ans =
1 0
0 1
>> full(Pauli('Y'))
ans =
0.0000 + 0.0000i 0.0000 - 1.0000i
0.0000 + 1.0000i 0.0000 + 0.0000i
>> Pauli('Z',1) % sparse Pauli Z operator
ans =
(1,1) 1
(2,2) -1
Multi-qubit examples
>> full(Pauli('XZI')) % the three-qubit Pauli operator X \otimes Z \otimes I
ans =
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 -1
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -1 0 0 0 0 0
0 0 0 -1 0 0 0 0
>> Pauli([0,1,2]) % the three-qubit Pauli operator I \otimes X \otimes Y
ans =
(4,1) 0 + 1.0000i
(3,2) 0 - 1.0000i
(2,3) 0 + 1.0000i
(1,4) 0 - 1.0000i
(8,5) 0 + 1.0000i
(7,6) 0 - 1.0000i
(6,7) 0 + 1.0000i
(5,8) 0 - 1.0000i
Source code
Click here to view this function's source code on github.
External links
- Pauli matrices at Wikipedia