PermutationOperator - Revision history

Nathaniel at 19:18, 23 September 2014

2014-09-23T19:18:39Z

Nathaniel at 19:10, 28 November 2012

2012-11-28T19:10:55Z

Nathaniel at 21:38, 20 November 2012

2012-11-20T21:38:19Z

Nathaniel at 20:40, 14 November 2012

2012-11-14T20:40:52Z

Nathaniel: Created page with "{{Function |name=PermutationOperator |desc=Produces a unitary operator that permutes subsystems |req=opt_args
PermuteSystems |rel=Swap
[[SwapOperator..."

2012-11-14T20:37:14Z

Created page with "{{Function |name=PermutationOperator |desc=Produces a unitary operator that permutes subsystems |req=opt_args<br />PermuteSystems |rel=Swap<br />[[SwapOperator..."

New page

{{Function
|name=PermutationOperator
|desc=Produces a [[unitary operator]] that permutes subsystems
|req=[[opt_args]]<br />[[PermuteSystems]]
|rel=[[Swap]]<br />[[SwapOperator]]
|upd=November 14, 2012
|v=1.00|}}
<tt>'''PermutationOperator'''</tt> is a [[List of functions|function]] that returns a [[unitary operator]] that permutes two or more subsystems. The unitary can be chosen to be full or sparse.

==Syntax==
* <tt>P = PermutationOperator(DIM,PERM)</tt>
* <tt>P = PermutationOperator(DIM,PERM,INV_PERM)</tt>
* <tt>P = PermutationOperator(DIM,PERM,INV_PERM,SP)</tt>

==Argument descriptions==
* <tt>DIM</tt>: A specification of the dimensions of the subsystems that <tt>P</tt> will act on. <tt>DIM</tt> can be provided in one of two ways:
** If <tt>DIM</tt> is a scalar, then all subsystems are assumed to have dimension <tt>DIM</tt>.
** If the subsystems have unequal dimensions, <tt>DIM</tt> should be a vector containing their dimensions.
* <tt>PERM</tt>: a permutation vector (i.e., a permutation of the vector <tt>1:n</tt>)
* <tt>INV_PERM</tt> (optional, default <tt>0</tt>): If equal to 0, this argument has no effect. If equal to 1, the permutation operator permutes subsystems according to the inverse of <tt>PERM</tt> rather than <tt>PERM</tt> itself.
* <tt>SP</tt> (optional, default <tt>0</tt>): If set equal to <tt>1</tt>, the permutation operator is sparse. If equal to <tt>0</tt>, the permutation operator is full.

==Examples==
===The standard [[swap operator]]===

The following code produces the operator that [[swap operator|swaps]] two [[qubit]]s (note that for simple uses like this one, it may be easier to just use the <tt>[[SwapOperator]]</tt> function):

<pre>
>> PermutationOperator(2,[2,1])

ans =

1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
</pre>

Similarly, the following code produces a sparse operator that swaps two [[qutrit]]s:

<pre>
>> PermutationOperator(3,[2,1],0,1)

ans =

(1,1) 1
(4,2) 1
(7,3) 1
(2,4) 1
(5,5) 1
(8,6) 1
(3,7) 1
(6,8) 1
(9,9) 1
</pre>

@@ Line 2: / Line 2: @@
 |name=PermutationOperator
 |desc=Produces a [[unitary operator]] that permutes subsystems
-|req=[[iden]]<br />[[opt_args]]<br />[[PermuteSystems]]
+|rel=[[PermuteSystems]]<br />[[Swap]]<br />[[SwapOperator]]<br />[[SymmetricProjection]]
-|rel=[[Swap]]<br />[[SwapOperator]]<br />[[SymmetricProjection]]
+|cat=[[List of functions#Permutations_and_symmetry_of_subsystems|Permutations and symmetry of subsystems]]
 |upd=November 28, 2012
-|v=1.01}}
+|v=0.50}}
 <tt>'''PermutationOperator'''</tt> is a [[List of functions|function]] that returns a [[unitary operator]] that permutes two or more subsystems. The unitary can be chosen to be full or sparse.
@@ Line 26: / Line 26: @@
 The following code produces the operator that [[swap operator|swaps]] two [[qubit]]s (note that for simple uses like this one, it may be easier to just use the <tt>[[SwapOperator]]</tt> function):
-<pre>
+<syntaxhighlight>
 >> PermutationOperator(2,[2,1])
@@ Line 35: / Line 35: @@
      1     0     0
      0     0     1
-</pre>
+</syntaxhighlight>
 Similarly, the following code produces a sparse operator that swaps two [[qutrit]]s:
-<pre>
+<syntaxhighlight>
 >> PermutationOperator(3,[2,1],0,1)
@@ Line 53: / Line 53: @@
     (6,8)        1
     (9,9)        1
-</pre>
+</syntaxhighlight>

@@ Line 3: / Line 3: @@
 |desc=Produces a [[unitary operator]] that permutes subsystems
 |req=[[opt_args]]<br />[[PermuteSystems]]
-|rel=[[Swap]]<br />[[SwapOperator]]
+|rel=[[Swap]]<br />[[SwapOperator]]<br />[[SymmetricProjection]]
 |upd=November 14, 2012
 |v=1.00|}}