Wolfram.com
WolframAlpha.com
WolframCloud.com
Wolfram Language
Example Repository
Ready-to-use examples for the Wolfram Language
Primary Navigation
Categories
Astronomy
Audio Processing
Calculus
Cellular Automata
Chemistry
Complex Systems
Computer Science
Computer Vision
Control Systems
Creative Arts
Data Science
Engineering
Finance & Economics
Finite Element Method
Food & Nutrition
Geography
Geometry
Graphs & Networks
Image Processing
Life Sciences
Machine Learning
Mathematics
Optimization
Physics
Puzzles and Recreation
Quantum Computation
Signal Processing
Social Sciences
System Modeling
Text & Language Processing
Time-Related Computation
Video Processing
Visualization & Graphics
Alphabetical List
Submit a New Resource
Learn More about
Wolfram Language
Related Pages
Related Categories
Computer Science
Physics
Quantum Computation
Symbolic Evolution of a Quantum State
Evolve a quantum state in time, symbolically
Example Notebook
Open in Cloud
Download Notebook
In the Wolfram Quantum Framework, quantum objects and operations can be defined symbolically and also numerically. In this regard, time evolution of quantum systems can be treated both symbolically and numerically.
Install and load the QuantumFramework paclet:
I
n
[
1
]
:
=
P
a
c
l
e
t
I
n
s
t
a
l
l
[
"
W
o
l
f
r
a
m
/
Q
u
a
n
t
u
m
F
r
a
m
e
w
o
r
k
"
]
N
e
e
d
s
[
"
W
o
l
f
r
a
m
`
Q
u
a
n
t
u
m
F
r
a
m
e
w
o
r
k
`
"
]
Define a symbolic 2D quantum state:
I
n
[
2
]
:
=
ψ
i
=
Q
u
a
n
t
u
m
S
t
a
t
e
[
{
α
,
β
}
]
;
Evolve it in time, by a time-independent Hamiltonian:
I
n
[
3
]
:
=
ψ
f
=
Q
u
a
n
t
u
m
E
v
o
l
v
e
[
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
]
,
ψ
i
,
t
]
;
Show the final state vector:
I
n
[
4
]
:
=
ψ
f
[
"
S
t
a
t
e
V
e
c
t
o
r
"
]
/
/
M
a
t
r
i
x
F
o
r
m
O
u
t
[
4
]
/
/
M
a
t
r
i
x
F
o
r
m
=
α
C
o
s
[
t
]
-
β
S
i
n
[
t
]
β
C
o
s
[
t
]
-
α
S
i
n
[
t
]
Evolve a mixed state, using a time-independent Hamiltonian:
I
n
[
5
]
:
=
ψ
f
=
Q
u
a
n
t
u
m
E
v
o
l
v
e
[
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
]
,
Q
u
a
n
t
u
m
S
t
a
t
e
[
{
"
B
l
o
c
h
V
e
c
t
o
r
"
,
{
1
,
1
,
1
}
/
2
}
]
,
t
]
;
Show the final state's density matrix:
I
n
[
6
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
/
@
N
o
r
m
a
l
[
ψ
f
[
"
D
e
n
s
i
t
y
M
a
t
r
i
x
"
]
]
/
/
M
a
t
r
i
x
F
o
r
m
O
u
t
[
6
]
/
/
M
a
t
r
i
x
F
o
r
m
=
1
4
(
2
+
C
o
s
[
2
t
]
+
S
i
n
[
2
t
]
)
-
1
4
(
+
C
o
s
[
2
t
]
-
S
i
n
[
2
t
]
)
1
4
(
-
+
C
o
s
[
2
t
]
-
S
i
n
[
2
t
]
)
1
4
(
2
-
C
o
s
[
2
t
]
-
S
i
n
[
2
t
]
)
Define a time-dependent Hamiltonian:
I
n
[
7
]
:
=
h
a
m
i
l
t
o
n
i
a
n
=
C
o
s
[
ω
t
]
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
]
;
Evolve an initial pure state, using the Hamiltonian:
I
n
[
8
]
:
=
ψ
f
=
Q
u
a
n
t
u
m
E
v
o
l
v
e
[
h
a
m
i
l
t
o
n
i
a
n
,
ψ
i
,
t
]
;
Show the final state vector:
I
n
[
9
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
[
N
o
r
m
a
l
[
ψ
f
[
"
S
t
a
t
e
V
e
c
t
o
r
"
]
]
]
O
u
t
[
9
]
=
α
C
o
s
S
i
n
[
t
ω
]
ω
-
β
S
i
n
S
i
n
[
t
ω
]
ω
,
β
C
o
s
S
i
n
[
t
ω
]
ω
-
α
S
i
n
S
i
n
[
t
ω
]
ω
Evolve a 3-qubit register state using Ising Hamiltonian
X
1
X
2
+
X
2
X
3
I
n
[
1
0
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
/
@
N
o
r
m
a
l
[
Q
u
a
n
t
u
m
E
v
o
l
v
e
[
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
X
"
]
+
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
X
"
{
2
,
3
}
]
,
t
]
[
"
S
t
a
t
e
V
e
c
t
o
r
"
]
]
O
u
t
[
1
0
]
=
{
2
C
o
s
[
t
]
,
0
,
0
,
-
C
o
s
[
t
]
S
i
n
[
t
]
,
0
,
-
2
S
i
n
[
t
]
,
-
C
o
s
[
t
]
S
i
n
[
t
]
,
0
}
External Links
QuantumEvolve
See Also
Wolfram/QuantumFramework
Numeric Evolution of a Quantum State
Publisher Information
Contributed by:
Wolfram Research, Quantum Computation Framework Team