Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumEvolve  |
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Details and Options
Examples
(9)
Basic Examples
(3)
Evolve a symbolic quantum state by a time-independent Hamiltonian, with independent variable :
t
In[1]:=
ψf=
["X"],
[{α,β}],t
 | QuantumEvolve |
 | QuantumOperator |
| QuantumState |
Out[1]=
QuantumState
 |  |
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Start with register state, without specifying any independent variable (note will be treated as formal parameter):
t
In[2]:=
 | QuantumEvolve |
| QuantumOperator |
Out[2]=
cos(t.)|0〉-sin(t.)|1〉
In[3]:=
U=
["X"],None,t
| QuantumEvolve |
| QuantumOperator |
Out[3]=
Cos[t]|0〉〈0|-Sin[t]|0〉〈1|-Sin[t]|1〉〈0|+Cos[t]|1〉〈1|
Evolve by above unitary:
|0〉
In[4]:=
U[]
Out[4]=
cos(t)|0〉-sin(t)|1〉
Define a time-dependent Hamiltonian:
In[1]:=
h=Cos[α]
["Z"]+Sin[α]Cos[ωt]
["X"]+Sin[ωt]
["Y"]
ω
1
2
| QuantumOperator |
ω
1
2
 | QuantumOperator |
| QuantumOperator |
Out[1]=
1
2
ω
1
1
2
ω
1
1
2
ω
1
1
2
ω
1
Define a symbolic initial state:
In[2]:=
ψi=
[{Cos[α/2],Sin[α/2]}]
| QuantumState |
Out[2]=
QuantumState
|  |
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Evolve the initial state with the Hamiltonian:
In[3]:=
ψf=
[h,ψi,t];
 | QuantumEvolve |
Show the final state vector, with :
λ=
-+2ωCos[α]-
2
ω
ω
1
2
ω
1
In[4]:=
FullSimplify[Normal[ψf["StateVector"]]]/.
_
λ,1_
1λOut[4]=
CosCosh+,SinCosh-
-tω
1
2
α
2
tλ
2
Sinh(ω-)
tλ
2
ω
1
λ
tω
2
α
2
tλ
2
Sinh(ω+)
tλ
2
ω
1
λ
Define a time-dependent Hamiltonian:
In[1]:=
hamiltonian=
["Z"]+γCos[t]
["X"];
1
2
ω
0
 | QuantumOperator |
ω
p
| QuantumOperator |
Given some numerical values for Hamiltonian parameters, find the final state:
In[2]:=
ω
0
8
10
ω
p
7
10
ω
p
| QuantumEvolve |
Show the state vector:
In[3]:=
ψf["StateVector"]//Normal
Out[3]=
InterpolatingFunction
[t],InterpolatingFunction
[t]
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Plot real and imaginary part of first element of state vector:
In[4]:=
ReImPlot[ψf["StateVector"]〚1〛,{t,tmin,tmax}]
Out[4]=
Generalizations & Extensions
(2)
Options
(3)
Possible Issues
(1)
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""