Pauli - Revision history

Nathaniel at 19:46, 14 January 2015

2015-01-14T19:46:51Z

← Older revision		Revision as of 19:46, 14 January 2015
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	\|name=Pauli		\|name=Pauli
	\|desc=Produces a Pauli operator		\|desc=Produces a Pauli operator
	\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]		\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]<br />[[PauliChannel]]
	\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]		\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]
	\|upd=November 27, 2014}}		\|upd=November 27, 2014}}

Nathaniel: typo correction

2014-11-27T21:53:17Z

typo correction

← Older revision		Revision as of 21:53, 27 November 2014
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	==Argument descriptions==		==Argument descriptions==
	* <tt>IND</tt>: An index indicating which Pauli operator you would like to be generated. Values of <tt>1</tt>, <tt>2</tt>, <tt>3</tt>, and <tt>0</tt> correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of <tt>'I'</tt>, <tt>'X'</tt>, <tt>'Y'</tt>, and <tt>'Z'</tt> are also accepted, and indicate the Pauli identity, X, Y, and Z operators, respectively. If <tt>IND</tt> is a vector then this function returns a multi-qubit Pauli operator whose action on the <tt>K</tt>-th qubit is the same as <tt>Pauli(K)</tt>.		* <tt>IND</tt>: An index indicating which Pauli operator you would like to be generated. Values of <tt>1</tt>, <tt>2</tt>, <tt>3</tt>, and <tt>0</tt> correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of <tt>'I'</tt>, <tt>'X'</tt>, <tt>'Y'</tt>, and <tt>'Z'</tt> are also accepted, and indicate the Pauli identity, X, Y, and Z operators, respectively. If <tt>IND</tt> is a vector then this function returns a multi-qubit Pauli operator whose action on the <tt>K</tt>-th qubit is the same as <tt>Pauli(IND(K))</tt>.
	* <tt>SP</tt> (optional, default 1): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.		* <tt>SP</tt> (optional, default 1): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.

Nathaniel at 21:52, 27 November 2014

2014-11-27T21:52:43Z

← Older revision		Revision as of 21:52, 27 November 2014
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	\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]		\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]
	\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]		\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]
	\|upd=~~December 18~~, ~~2013~~		\|upd=November 27, 2014}}
	~~\|v=0.50~~}}
	<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:		<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:

Nathaniel: Added multi-qubit functionality

2014-11-27T21:52:21Z

Added multi-qubit functionality

← Older revision		Revision as of 21:52, 27 November 2014
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	:<math>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}.</math>		:<math>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}.</math>

			This function can also produce multi-qubit Pauli operators.

	==Syntax==		==Syntax==
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	==Argument descriptions==		==Argument descriptions==
	* <tt>IND</tt>: An index indicating which Pauli operator you would like to be generated. Values of <tt>1</tt>, <tt>2</tt>, <tt>3</tt>, and <tt>0</tt> correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of <tt>'x'</tt>, <tt>'y'</tt>, and <tt>'z'</tt> are also accepted, and indicate the Pauli X, Y, and Z operators, respectively.		* <tt>IND</tt>: An index indicating which Pauli operator you would like to be generated. Values of <tt>1</tt>, <tt>2</tt>, <tt>3</tt>, and <tt>0</tt> correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of <tt>'I'</tt>, <tt>'X'</tt>, <tt>'Y'</tt>, and <tt>'Z'</tt> are also accepted, and indicate the Pauli identity, X, Y, and Z operators, respectively. If <tt>IND</tt> is a vector then this function returns a multi-qubit Pauli operator whose action on the <tt>K</tt>-th qubit is the same as <tt>Pauli(K)</tt>.
	* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.		* <tt>SP</tt> (optional, default 1): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.

	==Examples==		==Examples==
			===Single-qubit examples===
	<syntaxhighlight>		<syntaxhighlight>
	>> Pauli('x')		>> full(Pauli('X'))

	ans =		ans =
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	1 0		1 0

	>> Pauli(1)		>> full(Pauli(1))

	ans =		ans =
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	1 0		1 0

	>> Pauli(0)		>> full(Pauli(0))

	ans =		ans =
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	0 1		0 1

	>> Pauli('y')		>> full(Pauli('Y'))

	ans =		ans =
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	0.0000 + 1.0000i 0.0000 + 0.0000i		0.0000 + 1.0000i 0.0000 + 0.0000i

	>> Pauli('z',1) % sparse Pauli Z operator		>> Pauli('Z',1) % sparse Pauli Z operator

	ans =		ans =
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	(1,1) 1		(1,1) 1
	(2,2) -1		(2,2) -1
			</syntaxhighlight>

			===Multi-qubit examples===
			<syntaxhighlight>
			>> 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
	</syntaxhighlight>		</syntaxhighlight>

Nathaniel at 15:16, 29 September 2014

2014-09-29T15:16:09Z

← Older revision		Revision as of 15:16, 29 September 2014
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	\|name=Pauli		\|name=Pauli
	\|desc=Produces a Pauli operator		\|desc=Produces a Pauli operator
	~~\|req=[[opt_args]]~~
	\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]		\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]
			\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]
	\|upd=December 18, 2013		\|upd=December 18, 2013
	\|v=1.00}}		\|v=0.50}}
	<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:		<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:

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	==Examples==		==Examples==
	<~~pre~~>		<syntaxhighlight>
	>> Pauli('x')		>> Pauli('x')

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	(1,1) 1		(1,1) 1
	(2,2) -1		(2,2) -1
	</~~pre~~>		</syntaxhighlight>

			{{SourceCode\|name=Pauli}}

	==External links==		==External links==
	* [http://en.wikipedia.org/wiki/Pauli_matrices Pauli matrices] at Wikipedia		* [http://en.wikipedia.org/wiki/Pauli_matrices Pauli matrices] at Wikipedia

Nathaniel at 20:28, 18 December 2013

2013-12-18T20:28:24Z

← Older revision		Revision as of 20:28, 18 December 2013
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	\|desc=Produces a Pauli operator		\|desc=Produces a Pauli operator
	\|req=[[opt_args]]		\|req=[[opt_args]]
	\|rel=[[GellMann]]<br />[[GenPauli]]		\|rel=[[GellMann]]<br />[[GenGellMann]]<br />[[GenPauli]]
	\|upd=December 18, 2013		\|upd=December 18, 2013
	\|v=1.00}}		\|v=1.00}}

Nathaniel at 19:09, 18 December 2013

2013-12-18T19:09:11Z

← Older revision		Revision as of 19:09, 18 December 2013
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	<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:		<tt>'''Pauli'''</tt> is a [[List of functions\|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:

	$X = \begin{bmatrix}0 & 1\\ 1 & 0\end{bmatrix}, Y = \begin{bmatrix}0 & -i\\ i & 0\end{bmatrix}, Z = \begin{bmatrix}1 & 0\\ 0 & -1\end{bmatrix}, I = \begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}.$		:<math>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}.</math>

	==Syntax==		==Syntax==
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	0.0000 + 0.0000i 0.0000 - 1.0000i		0.0000 + 0.0000i 0.0000 - 1.0000i
	0.0000 + 1.0000i 0.0000 + 0.0000i		0.0000 + 1.0000i 0.0000 + 0.0000i

			>> Pauli('z',1) % sparse Pauli Z operator

			ans =

			(1,1) 1
			(2,2) -1
	</pre>		</pre>

	==External links==		==External links==
	* [http://en.wikipedia.org/wiki/Pauli_matrices Pauli matrices] at Wikipedia		* [http://en.wikipedia.org/wiki/Pauli_matrices Pauli matrices] at Wikipedia

Nathaniel at 18:38, 18 December 2013

2013-12-18T18:38:17Z

← Older revision		Revision as of 18:38, 18 December 2013
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	\|desc=Produces a Pauli operator		\|desc=Produces a Pauli operator
	\|req=[[opt_args]]		\|req=[[opt_args]]
	\|rel=[[GellMann]]		\|rel=[[GellMann]]<br />[[GenPauli]]
	~~\|req=~~[[GenPauli]]
	\|upd=December 18, 2013		\|upd=December 18, 2013
	\|v=1.00}}		\|v=1.00}}

Nathaniel: Created page with "{{Function |name=Pauli |desc=Produces a Pauli operator |req=opt_args |rel=GellMann |req=GenPauli |upd=December 18, 2013 |v=1.00}} `'''Pauli'''` is a [[List ..."

2013-12-18T18:37:52Z

Created page with "{{Function |name=Pauli |desc=Produces a Pauli operator |req=opt_args |rel=GellMann |req=GenPauli |upd=December 18, 2013 |v=1.00}} <tt>'''Pauli'''</tt> is a [[List ..."

New page

{{Function
|name=Pauli
|desc=Produces a Pauli operator
|req=[[opt_args]]
|rel=[[GellMann]]
|req=[[GenPauli]]
|upd=December 18, 2013
|v=1.00}}
<tt>'''Pauli'''</tt> is a [[List of functions|function]] that produces the 2-by-2 Pauli X, Y, Z, or identity operator, as defined here:

$X = \begin{bmatrix}0 & 1\\ 1 & 0\end{bmatrix}, Y = \begin{bmatrix}0 & -i\\ i & 0\end{bmatrix}, Z = \begin{bmatrix}1 & 0\\ 0 & -1\end{bmatrix}, I = \begin{bmatrix}1 & 0\\ 0 & 1\end{bmatrix}.$

==Syntax==
* <tt>P = Pauli(IND)</tt>
* <tt>P = Pauli(IND,SP)</tt>

==Argument descriptions==
* <tt>IND</tt>: An index indicating which Pauli operator you would like to be generated. Values of <tt>1</tt>, <tt>2</tt>, <tt>3</tt>, and <tt>0</tt> correspond to the Pauli X, Y, Z, and identity operators, respectively. Values of <tt>'x'</tt>, <tt>'y'</tt>, and <tt>'z'</tt> are also accepted, and indicate the Pauli X, Y, and Z operators, respectively.
* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that the Pauli operator produced should or should not be sparse.

==Examples==
<pre>
>> Pauli('x')

ans =

0 1
1 0

>> Pauli(1)

ans =

0 1
1 0

>> Pauli(0)

ans =

1 0
0 1

>> Pauli('y')

ans =

0.0000 + 0.0000i 0.0000 - 1.0000i
0.0000 + 1.0000i 0.0000 + 0.0000i
</pre>

==External links==
* [http://en.wikipedia.org/wiki/Pauli_matrices Pauli matrices] at Wikipedia