Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
Ket  |  |
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| Ket[spec,{ s 1 s 2 Ket[spec,s] KetRegulate s 1 s 2 KetRegulate | | ||||
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Details and Options
Examples
(10)
Basic Examples
(8)
Consider a register of three qubits. A typical quantum state looks as follows.
In[1]:=
in=Ket[{0,1,1}]-I*Ket[{1,0,0}]
Out[1]=
|0,1,1〉-|1,0,0〉
We want to operate a string of Pauli operators.
In[2]:=
op=Pauli[{3,2,0}]
Out[2]=
Z⊗Y⊗I
Operate the above operate on the input state.
In[3]:=
out=op**in
Out[3]=
-|0,0,1〉-|1,1,0〉
In many case, you do not have to type the computational basis states.
In[4]:=
bs=Basis[3]
Out[4]=
{|0,0,0〉,|0,0,1〉,|0,1,0〉,|0,1,1〉,|1,0,0〉,|1,0,1〉,|1,1,0〉,|1,1,1〉}
Consider a register of qubits. We will refer to the register with symbol S.
In[1]:=
Let[Qubit,S]
These three expressions are equivalent.
In[2]:=
Ket[S[1]1]Ket[S[1,$]1]Ket[S[1,$,$]1]
Out[2]=
1
S
1
Out[2]=
1
S
1
Out[2]=
1
S
1
Consider a superposition state.
In[3]:=
in=Ket[S@{1,2,3}{0,1,1}]-I*Ket[S@{1,2,3}{1,0,0}]
Out[3]=
-
0
S
1
1
S
2
1
S
3
1
S
1
0
S
2
0
S
3
Consider a string of Pauli operators.
In[4]:=
op=S[1,3]**S[2,2]
Out[4]=
Z
S
1
Y
S
2
Operate the above operator on the input state.
In[5]:=
out=op**in
Out[5]=
--
0
S
1
0
S
2
1
S
3
1
S
1
1
S
2
0
S
3
Construct the computational basis.
In[6]:=
Basis[S@{1,2,3}]
Out[6]=
,,,,,,,
0
S
1
0
S
2
0
S
3
0
S
1
0
S
2
1
S
3
0
S
1
1
S
2
0
S
3
0
S
1
1
S
2
1
S
3
1
S
1
0
S
2
0
S
3
1
S
1
0
S
2
1
S
3
1
S
1
1
S
2
0
S
3
1
S
1
1
S
2
1
S
3
Q3: Symbolic Quantum Simulation assumes default values for any species in when the values of the species are not specified explicitly, and hence the following two expressions are equivalent.
In[1]:=
u=Ket[S[1]0]+IKet[S[1]1]
Out[1]=
+
0
S
1
1
S
1
In[2]:=
v=Ket[]+IKet[S[1]1]
Out[2]=
|␣〉+
1
S
1
In[3]:=
u-v//Elaborate
Out[3]=
0
The converts Ket into a more human readable form.
KetRegulate
In[4]:=
w=v//KetRegulate
Out[4]=
+
0
S
1
1
S
1
In[5]:=
w//KetTrim
Out[5]=
|␣〉+
1
S
1
This shows an advanced method to specify a logical basis state for labelled systems.
In[1]:=
Ket[S[{1,2,3,4}]{0,0,1,0},S[5]0]
Out[1]=
0
S
1
0
S
2
1
S
3
0
S
4
0
S
5
In[2]:=
ss=S[{1,2,3}]Ket[ss{0,0,1}]Ket[ss1]
Out[2]=
{,,}
X
S
Y
S
Z
S
Out[2]=
0
S
1
0
S
2
1
S
3
Out[2]=
1
S
1
1
S
2
1
S
3
In[3]:=
bs=Basis[S[{1,2}]]
Out[3]=
,,,
0
S
1
0
S
2
0
S
1
1
S
2
1
S
1
0
S
2
1
S
1
1
S
2
In[4]:=
vw=S[2,1]**S[1,1]**vu=S[3,2]**w
Out[4]=
|␣〉+
1
S
1
Out[4]=
+
0
S
1
1
S
2
1
S
1
1
S
2
Out[4]=
-+
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
In[5]:=
u//KetRegulatematU=Matrix[u];matU//MatrixFormuu=u⊗Ket[S[2]1]matUU=Matrix[uu];matUU//MatrixForm
Out[5]=
-+
0
S
1
1
S
2
1
S
3
1
S
1
1
S
2
1
S
3
Out[5]//MatrixForm=
0 |
0 |
0 |
-1 |
0 |
0 |
0 |
|
Out[7]//InputForm=
-Ket[<|S[$] -> 0, S[2, $] -> 1, S[3, $] -> 1|>] +
I*Ket[<|S[$] -> 1, S[2, $] -> 1, S[3, $] -> 1|>]
I*Ket[<|S[$] -> 1, S[2, $] -> 1, S[3, $] -> 1|>]
You can add additional elements or modifies existing elements.
You can extract the bit values by giving the particular qubit as an input.
Here $ is explicitly specified.
To the column vector form, then back to the Ket form.
To be compared with the KetForm[]
Sometime one has to manually put spin values. In such a case, the following form will be useful to avoid tedious typing. Notice the Null input at the end, which will be automatically converted to the default value.
It is equivalent to
One can mix up different kinds of Species as well.