Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
Bra |
Details and Options
Examples
(5)
Basic Examples
(5)
Consider a state vector for unlabeled qubits.
In[1]:=
v=Ket[0,1]
Out[1]=
|0,1〉
The corresponding dual vector is denoted by .
Bra[…]
In[2]:=
dv=Dagger[v]
Out[2]=
〈0,1|
You can specify it explicitly.
In[3]:=
Bra[0,1]
Out[3]=
〈0,1|
The Hermitian product 〈u,v〉 between two vectors can be obtained by the non-commutative multiplication of and .
〈u|
|v〉
In[4]:=
u=Ket[0,1]+IKet[1,0]v=Ket[0,1]+Ket[1,0]
Out[4]=
|0,1〉+|1,0〉
Out[4]=
|0,1〉+|1,0〉
In[5]:=
Dagger[u]
Out[5]=
〈0,1|-〈1,0|
In[6]:=
Dagger[u]**v
Out[6]=
1-
Now consider a system of labeled qubits.
In[1]:=
Let[Qubit,S]
In[2]:=
Bra[S[1]1]Bra[S[1,$]1]Bra[S[1,$]1]Bra[S[1,$,$]1]
Out[2]=
1
S
1
Out[2]=
1
S
1
Out[2]=
1
S
1
Out[2]=
1
S
1
In[3]:=
u=Bra[S[1]1]v=Bra[u,S[3]1]w=v[S[2]1]w[S[2]]
Out[3]=
1
S
1
Out[3]=
1
S
1
1
S
3
Out[3]=
1
S
1
1
S
2
1
S
3
Out[3]=
1
By default, the Bra expression is optimized for calculation, and hence it may look weird at first.
In[4]:=
v=Bra[S[1]0]+IBra[S[1]1]
Out[4]=
+
0
S
1
1
S
1
The KetRegulate of a Bra may be more human readable, but it can slow down the subsequent calculations.
In[5]:=
v=Bra[]+IBra[S[1]1]
Out[5]=
〈␣|+
1
S
1
In[6]:=
w=v//KetRegulatew//KetTrim
Out[6]=
+
0
S
1
1
S
1
Out[6]=
〈␣|+
1
S
1
In[7]:=
Bra[S[{1,2,3,4}]{0,0,1,0},S[5]0]
Out[7]=
0
S
1
0
S
2
1
S
3
0
S
4
0
S
5
In[8]:=
ss=S[{1,2,3}]Bra[ss{0,0,1}]Bra[ss1]
Out[8]=
{,,}
x
S
y
S
z
S
Out[8]=
0
S
1
0
S
2
1
S
3
Out[8]=
1
S
1
1
S
2
1
S
3
In[9]:=
vw=v**S[2,1]**S[1,1]u=w**S[3,2]
Out[9]=
〈␣|+
1
S
1
Out[9]=
+
0
S
1
1
S
2
1
S
1
1
S
2
Out[9]=
-
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
In[10]:=
u//KetRegulatematU=Matrix[u];matU//MatrixFormuu=u⊗Bra[S[2]1]matUU=Matrix[uu];matUU//MatrixForm
Out[10]=
-
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
Out[10]//MatrixForm=
0 |
0 |
0 |
1 |
0 |
0 |
0 |
- |
Out[10]=
-
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
Out[10]//MatrixForm=
0 |
0 |
0 |
1 |
0 |
0 |
0 |
- |
In[11]:=
uu=ExpressionFor[Conjugate@matU,{S[1],S[2],S[3]}]Dagger@uu
Out[11]=
+
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
You can add additional elements or modifies existing elements.
Accessing the values