Nathaniel: Created page with "{{Function |name=WState |desc=Generates a (generalized) W-state |rel=DickeState
GHZState
MaxEntangled |cat=List of functions#Special_states,_vectors,_a..."

2014-12-24T16:20:24Z

Created page with "{{Function |name=WState |desc=Generates a (generalized) W-state |rel=DickeState<br />GHZState<br />MaxEntangled |cat=List of functions#Special_states,_vectors,_a..."

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{{Function
|name=WState
|desc=Generates a (generalized) W-state
|rel=[[DickeState]]<br />[[GHZState]]<br />[[MaxEntangled]]
|cat=[[List of functions#Special_states,_vectors,_and_operators|Special states, vectors, and operators]]
|upd=December 24, 2014}}
<tt>'''WState'''</tt> is a [[List of functions|function]] that returns a [http://en.wikipedia.org/wiki/W_state W-state] on a given number of qubits. For example, the usual $3$-qubit W-state is $\frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle)$. More generally, the W-state on $q$ qudits is $\frac{1}{\sqrt{q}}(|10\cdots 00\rangle + |01\cdots 00\rangle + \cdots + |00\cdots 01\rangle)$. The output of this function is a sparse vector.

==Syntax==
* <tt>W_STATE = WState(Q)</tt>
* <tt>W_STATE = WState(Q,COEFF)</tt>

==Argument descriptions==
* <tt>Q</tt>: The number of qubits.
* <tt>COEFF</tt> (optional, default <tt>[1,1,...,1]/sqrt(Q)</tt>): A vector whose $j$-th entry is the coefficient of the term $|0\rangle^{\otimes (j-1)} \otimes |1\rangle \otimes |0\rangle^{\otimes q-j}$ in the sum that defines the W-state.

==Examples==
===3-qubit W-state===
The following code generates the usual 3-qubit GHZ state:
<syntaxhighlight>
>> full(WState(3))

ans =

0
0.5774
0.5774
0
0.5774
0
0
0
</syntaxhighlight>

===A generalized W-state===
The following code generates the following generalized 4-qubit W-state:
: <math>\frac{1}{\sqrt{30}}\big( |1000\rangle + 2|0100\rangle + 3|0010\rangle + 4|0001\rangle \big).</math>
<syntaxhighlight>
>> WState(4,[1,2,3,4]/sqrt(30))

ans =

(2,1) 0.7303
(3,1) 0.5477
(5,1) 0.3651
(9,1) 0.1826
</syntaxhighlight>

===A very large W-state===
This script has no trouble creating W-states on very large numbers of qubits. The following code generates the 30-qubit W-state:
<syntaxhighlight>
>> WState(30)

ans =

(2,1) 0.1826
(3,1) 0.1826
(5,1) 0.1826
(9,1) 0.1826
(17,1) 0.1826
(33,1) 0.1826
(65,1) 0.1826
(129,1) 0.1826
(257,1) 0.1826
(513,1) 0.1826
(1025,1) 0.1826
(2049,1) 0.1826
(4097,1) 0.1826
(8193,1) 0.1826
(16385,1) 0.1826
(32769,1) 0.1826
(65537,1) 0.1826
(131073,1) 0.1826
(262145,1) 0.1826
(524289,1) 0.1826
(1048577,1) 0.1826
(2097153,1) 0.1826
(4194305,1) 0.1826
(8388609,1) 0.1826
(16777217,1) 0.1826
(33554433,1) 0.1826
(67108865,1) 0.1826
(134217729,1) 0.1826
(268435457,1) 0.1826
(536870913,1) 0.1826
</syntaxhighlight>

{{SourceCode|name=WState}}

WState - Revision history

Nathaniel: Created page with "{{Function |name=WState |desc=Generates a (generalized) W-state |rel=DickeStateGHZStateMaxEntangled |cat=List of functions#Special_states,_vectors,_a..."

Nathaniel: Created page with "{{Function |name=WState |desc=Generates a (generalized) W-state |rel=DickeState
GHZState
MaxEntangled |cat=List of functions#Special_states,_vectors,_a..."