Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
Qudit  |
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Details and Options
Examples
(3)
Basic Examples
(2)
Choose a symbol to refer to the system of qudits.
In[1]:=
Let[Qudit,A]
This refers to the specific qudit.
In[2]:=
A[1,$]
Out[2]=
A
1
Consider the operator on the qudit that induces a transition from level 1 to level 2.
In[3]:=
op=A[1,12]
Out[3]=
(|2〉〈1|)
1
In[4]:=
in=Total@Basis@A[1]
Out[4]=
++
0
A
1
1
A
1
2
A
1
In[5]:=
op**in
Out[5]=
2
A
1
Refers to a Weyl operator on the qudit.
In[6]:=
op=A[1,$@{1,2}]
Out[6]=
1
X
1
2
Z
1
In[7]:=
in=Total@Basis@A[1]
Out[7]=
++
0
A
1
1
A
1
2
A
1
In[8]:=
op**in
Out[8]=
2/3
(-1)
0
A
1
1
A
1
1/3
(-1)
2
A
1
The Hermitian conjugate of the elementary operator on a qudit.
In[9]:=
Dagger@A[1,12]
Out[9]=
(|1〉〈2|)
1
Test where a given symbol is associated with a qudit.
In[10]:=
QuditQ[A]QuditQ[A[1,$]]QuditQ[A[1,12]]
Out[10]=
True
Out[10]=
True
Out[10]=
True
Check the dimension of qudits.
In[11]:=
Dimension[A]Dimension[A[1,12]]Dimension[A[{1,2},]]
Out[11]=
3
Out[11]=
3
Out[11]=
{3,3}
If the operator specification is out of the range defined by the dimension, it is treated as a null operator.
In[12]:=
A[1,13]A[1,11]
::range
A
1
Out[12]=
0
Out[12]=
(|1〉〈1|)
1
You can also create a qudit operator collectively. This shows how to species two transition operators at the same time.
In[13]:=
A[1,1{0,2}]
Out[13]=
{,}
(|0〉〈1|)
1
(|2〉〈1|)
1
Similarly,
In[14]:=
jj={0,1,2}rj=RotateLeft@jjA[1,jjrj]
Out[14]=
{0,1,2}
Out[14]=
{1,2,0}
Out[14]=
{,,}
(|1〉〈0|)
1
(|2〉〈1|)
1
(|0〉〈2|)
1
Qudit operators may act on qudit operators. If two qudit operators belong to the same qudit, the result is simplified.
In[15]:=
A[1,12]**A[1,01]
Out[15]=
(|2〉〈0|)
1
In[16]:=
A[1,22]**A[1,01]
Out[16]=
0
In[17]:=
A[1,11]**A[1,01]
Out[17]=
(|1〉〈0|)
1
In[18]:=
v=A[1,01]**Ket[]A[1,22]**vA[1,22]**A[1,01]**Ket[]
Out[18]=
1
A
1
Out[18]=
0
Out[18]=
0
In[19]:=
A[1,01]**A[2,12]A[2,12]**A[1,01]
Out[19]=
(|1〉〈0|)
1
(|2〉〈1|)
2
Out[19]=
(|1〉〈0|)
1
(|2〉〈1|)
2
In[1]:=
Let[Qudit,A]
In[2]:=
FlavorCap@Thread[A[{1,2}]3]
Out[2]=
{3,3}
A
1
A
2
In[3]:=
%//InputForm
Out[3]//InputForm=
{A[1, $] -> 3, A[2, $] -> 3}
The level specification should be within the dimension.
In[4]:=
v=Ket[A[1]3]
::qudit
A
1
Out[4]=
$Failed
In[5]:=
v=Ket[A[1]2,A[{1,2}]2,A[{3,4}]1]
Out[5]=
2
A
1
2
A
2
1
A
3
1
A
4
In[6]:=
A[1,20]**vA[1,21]**v
Out[6]=
2
A
2
1
A
3
1
A
4
Out[10]//InputForm=
Ket[<|A[1, $] -> 2, A[2, $] -> 2, A[3, $] -> 1, A[4, $] -> 1|>]