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Computer Science
Physics
Quantum Computation
Symbolic Evolution of a Quantum State
Evolve a quantum state in time, symbolically
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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:
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P
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Define a symbolic 2D quantum state:
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=
ψ
i
=
Q
u
a
n
t
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m
S
t
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[
{
α
,
β
}
]
;
Evolve it in time, by a time-independent Hamiltonian:
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:
=
ψ
f
=
Q
u
a
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v
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[
Q
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O
p
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r
a
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o
r
[
"
X
"
]
,
ψ
i
,
t
]
;
Show the final state vector:
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:
=
ψ
f
[
"
S
t
a
t
e
V
e
c
t
o
r
"
]
/
/
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a
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i
x
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o
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O
u
t
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4
]
/
/
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a
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i
x
F
o
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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
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5
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:
=
ψ
f
=
Q
u
a
n
t
u
m
E
v
o
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v
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[
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
]
,
Q
u
a
n
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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
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:
=
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
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[
2
t
]
)
1
4
(
2
-
C
o
s
[
2
t
]
-
S
i
n
[
2
t
]
)
Define a time-dependent Hamiltonian:
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:
=
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
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8
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:
=
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
[
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=
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
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0
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:
=
F
u
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i
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/
@
N
o
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m
a
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[
Q
u
a
n
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u
m
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v
o
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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
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[
t
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,
0
,
-
2
S
i
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[
t
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,
-
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