Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumEvolve  |
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Details and Options
Examples
(5)
Basic Examples
(4)
Evolve a symbolic quantum state by a time-independent Hamiltonian, with independent variable :
t
In[1]:=
ψf=
["X"],
[{α,β}],t;
 | QuantumEvolve |
 | QuantumOperator |
| QuantumState |
Show the final state vector:
In[2]:=
ψf["StateVector"]//MatrixForm
Out[2]//MatrixForm=
αCos[t]-βSin[t] |
βCos[t]-αSin[t] |
Start with register state, without specifying any independent variable (note will be treated as formal parameter):
t
In[3]:=
| QuantumEvolve |
 | QuantumOperator |
Out[3]//MatrixForm=
Cos[t.] |
-Sin[t.] |
In[4]:=
U=
["X"],None,t
 | QuantumEvolve |
| QuantumOperator |
Out[4]=
QuantumOperator
 |  |
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Define a time-dependent Hamiltonian:
In[1]:=
hamiltonian=Cos[α]
["Z"]+Sin[α]Cos[ωt]
["X"]+Sin[ωt]
["Y"];hamiltonian["Matrix"]//MatrixForm
ω
1
2
| QuantumOperator |
ω
1
2
 | QuantumOperator |
| QuantumOperator |
Out[1]//MatrixForm=
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 |
Evolve the initial state with the Hamiltonian:
In[3]:=
ψf=
[hamiltonian,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
Evolution operator of a given Hamiltonian:
In[1]:=
u=
["X"],None,t
| QuantumEvolve |
| QuantumOperator |
Out[1]=
QuantumOperator
|  |
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In[2]:=
u["Matrix"]//MatrixForm
Out[2]//MatrixForm=
Cos[t] | -Sin[t] |
-Sin[t] | Cos[t] |
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]=
Possible Issues
(1)
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