Swap - Revision history

Nathaniel at 18:13, 12 November 2014

2014-11-12T18:13:19Z

← Older revision		Revision as of 18:13, 12 November 2014
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	\|upd=November 12, 2014		\|upd=November 12, 2014
	\|v=0.60}}		\|v=0.60}}
	<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.		<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a quantum state or operator live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.

	==Syntax==		==Syntax==
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	==Argument descriptions==		==Argument descriptions==
	* <tt>X</tt>: a vector (e.g., a [[pure quantum state]]) or a matrix to have its subsystems permuted		* <tt>X</tt>: a vector (e.g., a pure quantum state) or a matrix to have its subsystems permuted
	* <tt>SYS</tt> (optional, default <tt>[1,2]</tt>): a 1-by-2 vector containing the indices of the subsystems to be swapped		* <tt>SYS</tt> (optional, default <tt>[1,2]</tt>): a 1-by-2 vector containing the indices of the subsystems to be swapped
	* <tt>DIM</tt> (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that <tt>X</tt> lives on. <tt>DIM</tt> can be provided in one of three ways:		* <tt>DIM</tt> (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that <tt>X</tt> lives on. <tt>DIM</tt> can be provided in one of three ways:

Nathaniel: Updated to v0.60 (reversed order of SYS and DIM arguments)

2014-11-12T18:12:52Z

Updated to v0.60 (reversed order of SYS and DIM arguments)

← Older revision		Revision as of 18:12, 12 November 2014
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	{{Function		{{Function
	\|name=Swap		\|name=Swap
	\|desc=Swaps two subsystems within a [[state]] or [[operator]]		\|desc=Swaps two subsystems within a state or operator
	\|rel=[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[SwapOperator]]		\|rel=[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[SwapOperator]]
	\|cat=[[List of functions#Permutations_and_symmetry_of_subsystems\|Permutations and symmetry of subsystems]]		\|cat=[[List of functions#Permutations_and_symmetry_of_subsystems\|Permutations and symmetry of subsystems]]
	\|upd=November 15, ~~2012~~		\|upd=November 12, 2014
	\|v=0.50}}		\|v=0.60}}
	<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.		<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.

	==Syntax==		==Syntax==
	* <tt>SX = Swap(X)</tt>		* <tt>SX = Swap(X)</tt>
	* <tt>SX = Swap(X,~~DIM~~)</tt>		* <tt>SX = Swap(X,SYS)</tt>
	* <tt>SX = Swap(X,DIM~~,SYS~~)</tt>		* <tt>SX = Swap(X,SYS,DIM)</tt>
	* <tt>SX = Swap(X,DIM~~,SYS~~,ROW_ONLY)</tt>		* <tt>SX = Swap(X,SYS,DIM,ROW_ONLY)</tt>

	==Argument descriptions==		==Argument descriptions==
	* <tt>X</tt>: a vector (e.g., a [[pure quantum state]]) or a matrix to have its subsystems permuted		* <tt>X</tt>: a vector (e.g., a [[pure quantum state]]) or a matrix to have its subsystems permuted
			* <tt>SYS</tt> (optional, default <tt>[1,2]</tt>): a 1-by-2 vector containing the indices of the subsystems to be swapped
	* <tt>DIM</tt> (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that <tt>X</tt> lives on. <tt>DIM</tt> can be provided in one of three ways:		* <tt>DIM</tt> (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that <tt>X</tt> lives on. <tt>DIM</tt> can be provided in one of three ways:
	** If <tt>DIM</tt> is a scalar, it is assumed that <tt>X</tt> lives on the tensor product of two spaces, the first of which has dimension <tt>DIM</tt> and the second of which has dimension <tt>length(X)/DIM</tt>.		** If <tt>DIM</tt> is a scalar, it is assumed that <tt>X</tt> lives on the tensor product of two spaces, the first of which has dimension <tt>DIM</tt> and the second of which has dimension <tt>length(X)/DIM</tt>.
	** If $X \in M_{n_1} \otimes \cdots \otimes M_{n_p}$ then <tt>DIM</tt> should be a row vector containing the dimensions (i.e., <tt>DIM = [n_1, ..., n_p]</tt>).		** If $X \in M_{n_1} \otimes \cdots \otimes M_{n_p}$ then <tt>DIM</tt> should be a row vector containing the dimensions (i.e., <tt>DIM = [n_1, ..., n_p]</tt>).
	** If the subsystems aren't square (i.e., $X \in M_{m_1, n_1} \otimes \cdots \otimes M_{m_p, n_p}$) then <tt>DIM</tt> should be a matrix with two rows. The first row of <tt>DIM</tt> should contain the row dimensions of the subsystems (i.e., the m<sub>i</sub>'s) and its second row should contain the column dimensions (i.e., the n<sub>i</sub>'s). In other words, you should set <tt>DIM = [m_1, ..., m_p; n_1, ..., n_p]</tt>.		** If the subsystems aren't square (i.e., $X \in M_{m_1, n_1} \otimes \cdots \otimes M_{m_p, n_p}$) then <tt>DIM</tt> should be a matrix with two rows. The first row of <tt>DIM</tt> should contain the row dimensions of the subsystems (i.e., the m<sub>i</sub>'s) and its second row should contain the column dimensions (i.e., the n<sub>i</sub>'s). In other words, you should set <tt>DIM = [m_1, ..., m_p; n_1, ..., n_p]</tt>.
	* <tt>SYS</tt> (optional, default <tt>[1,2]</tt>): a 1-by-2 vector containing the indices of the subsystems to be swapped
	* <tt>ROW_ONLY</tt> (optional, default <tt>0</tt>): If set equal to <tt>1</tt>, only the rows of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on the left by <tt>[[SwapOperator\|SwapOperator(DIM,SYS)]]</tt>). If equal to <tt>0</tt>, both the rows and columns of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on both the left and right by the swap operator).		* <tt>ROW_ONLY</tt> (optional, default <tt>0</tt>): If set equal to <tt>1</tt>, only the rows of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on the left by <tt>[[SwapOperator\|SwapOperator(DIM,SYS)]]</tt>). If equal to <tt>0</tt>, both the rows and columns of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on both the left and right by the swap operator).

Nathaniel at 19:22, 23 September 2014

2014-09-23T19:22:44Z

@@ Line 2: / Line 2: @@
 |name=Swap
 |desc=Swaps two subsystems within a [[state]] or [[operator]]
-|req=[[opt_args]]<br />[[PermuteSystems]]
+|rel=[[PermutationOperator]]<br />[[PermuteSystems]]<br />[[SwapOperator]]
-|rel=[[PermutationOperator]]<br />[[SwapOperator]]
+|cat=[[List of functions#Permutations_and_symmetry_of_subsystems|Permutations and symmetry of subsystems]]
 |upd=November 15, 2012
-|v=1.01}}
+|v=0.50}}
 <tt>'''Swap'''</tt> is a [[List of functions|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether &ndash; the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.
@@ Line 24: / Line 24: @@
 ==Examples==
-Please add examples here.
+The following code constructs a 4-by-4 matrix (thought of as an operator in $M_2 \otimes M_2$) and then swaps the two subsystems, which is equivalent to multiplying on the left and right by the swap operator:

Nathaniel at 20:37, 15 November 2012

2012-11-15T20:37:11Z

← Older revision		Revision as of 20:37, 15 November 2012
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	\|req=[[opt_args]]<br />[[PermuteSystems]]		\|req=[[opt_args]]<br />[[PermuteSystems]]
	\|rel=[[PermutationOperator]]<br />[[SwapOperator]]		\|rel=[[PermutationOperator]]<br />[[SwapOperator]]
	\|upd=November 14, 2012		\|upd=November 15, 2012
	\|v=1.~~00\|~~}}		\|v=1.01}}
	<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.		<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.

Nathaniel: typos

2012-11-15T00:02:33Z

typos

← Older revision		Revision as of 00:02, 15 November 2012
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	\|upd=November 14, 2012		\|upd=November 14, 2012
	\|v=1.00\|}}		\|v=1.00\|}}
	<tt>'''Swap'''</tt> is a function ~~the swap~~ the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether -- the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.		<tt>'''Swap'''</tt> is a [[List of functions\|function]] that swaps the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether – the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.

	==Syntax==		==Syntax==

Nathaniel: Created page with "{{Function |name=Swap |desc=Swaps two subsystems within a state or operator |req=opt_args
PermuteSystems |rel=PermutationOperator
[[SwapOperator]..."

2012-11-14T21:28:27Z

Created page with "{{Function |name=Swap |desc=Swaps two subsystems within a state or operator |req=opt_args PermuteSystems |rel=PermutationOperator [[SwapOperator]..."

New page

{{Function
|name=Swap
|desc=Swaps two subsystems within a [[state]] or [[operator]]
|req=[[opt_args]] [[PermuteSystems]]
|rel=[[PermutationOperator]] [[SwapOperator]]
|upd=November 14, 2012
|v=1.00|}}
<tt>'''Swap'''</tt> is a function the swap the position of two subsystems in the space on which a [[quantum state]] or [[operator]] live. Note that the state or operator can have more than two subsystems altogether -- the remaining subsystems are not affected. To permute the positions of more than two subsystems, use the <tt>[[PermuteSystems]]</tt> function.

==Syntax==
* <tt>SX = Swap(X)</tt>
* <tt>SX = Swap(X,DIM)</tt>
* <tt>SX = Swap(X,DIM,SYS)</tt>
* <tt>SX = Swap(X,DIM,SYS,ROW_ONLY)</tt>

==Argument descriptions==
* <tt>X</tt>: a vector (e.g., a [[pure quantum state]]) or a matrix to have its subsystems permuted
* <tt>DIM</tt> (optional, by default has all subsystems of equal dimension): A specification of the dimensions of the subsystems that <tt>X</tt> lives on. <tt>DIM</tt> can be provided in one of three ways:
** If <tt>DIM</tt> is a scalar, it is assumed that <tt>X</tt> lives on the tensor product of two spaces, the first of which has dimension <tt>DIM</tt> and the second of which has dimension <tt>length(X)/DIM</tt>.
** If $X \in M_{n_1} \otimes \cdots \otimes M_{n_p}$ then <tt>DIM</tt> should be a row vector containing the dimensions (i.e., <tt>DIM = [n_1, ..., n_p]</tt>).
** If the subsystems aren't square (i.e., $X \in M_{m_1, n_1} \otimes \cdots \otimes M_{m_p, n_p}$) then <tt>DIM</tt> should be a matrix with two rows. The first row of <tt>DIM</tt> should contain the row dimensions of the subsystems (i.e., the mi's) and its second row should contain the column dimensions (i.e., the ni's). In other words, you should set <tt>DIM = [m_1, ..., m_p; n_1, ..., n_p]</tt>.
* <tt>SYS</tt> (optional, default <tt>[1,2]</tt>): a 1-by-2 vector containing the indices of the subsystems to be swapped
* <tt>ROW_ONLY</tt> (optional, default <tt>0</tt>): If set equal to <tt>1</tt>, only the rows of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on the left by <tt>[[SwapOperator|SwapOperator(DIM,SYS)]]</tt>). If equal to <tt>0</tt>, both the rows and columns of <tt>X</tt> are permuted (this is equivalent to multiplying <tt>X</tt> on both the left and right by the swap operator).

==Examples==
Please add examples here.