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Computer Science
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Quantum Computation
Symbolic Computation for Quantum Circuits
Example Notebook
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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 BooleanOracle circuit for a Boolean function:
I
n
[
2
]
:
=
q
c
=
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
{
"
B
o
o
l
e
a
n
O
r
a
c
l
e
"
,
a
&
&
!
b
|
|
c
&
&
d
}
]
;
q
c
[
"
D
i
a
g
r
a
m
"
]
O
u
t
[
2
]
=
Transform a superposition using the corresponding BooleanOracle circuit:
I
n
[
3
]
:
=
q
c
[
α
Q
u
a
n
t
u
m
S
t
a
t
e
[
"
1
1
1
1
0
"
]
+
β
Q
u
a
n
t
u
m
S
t
a
t
e
[
"
1
1
0
1
0
"
]
]
/
/
T
r
a
d
i
t
i
o
n
a
l
F
o
r
m
O
u
t
[
3
]
/
/
T
r
a
d
i
t
i
o
n
a
l
F
o
r
m
=
β
|
1
1
0
1
0
〉
+
α
|
1
1
1
1
1
〉
Define a Multiplexer using symbolic rotations:
I
n
[
4
]
:
=
q
c
=
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
{
"
M
u
l
t
i
p
l
e
x
e
r
"
,
{
"
R
X
"
,
θ
1
}
,
{
"
R
X
"
,
θ
2
}
,
{
"
R
X
"
,
θ
3
}
,
{
"
R
X
"
,
θ
4
}
}
]
;
q
c
[
"
D
i
a
g
r
a
m
"
]
O
u
t
[
4
]
=
Show the corresponding matrix:
I
n
[
5
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
[
N
o
r
m
a
l
[
q
c
[
"
M
a
t
r
i
x
"
]
]
]
/
/
M
a
t
r
i
x
F
o
r
m
O
u
t
[
5
]
/
/
M
a
t
r
i
x
F
o
r
m
=
C
o
s
θ
1
2
-
S
i
n
θ
1
2
0
0
0
0
0
0
-
S
i
n
θ
1
2
C
o
s
θ
1
2
0
0
0
0
0
0
0
0
C
o
s
θ
2
2
-
S
i
n
θ
2
2
0
0
0
0
0
0
-
S
i
n
θ
2
2
C
o
s
θ
2
2
0
0
0
0
0
0
0
0
C
o
s
θ
3
2
-
S
i
n
θ
3
2
0
0
0
0
0
0
-
S
i
n
θ
3
2
C
o
s
θ
3
2
0
0
0
0
0
0
0
0
C
o
s
θ
4
2
-
S
i
n
θ
4
2
0
0
0
0
0
0
-
S
i
n
θ
4
2
C
o
s
θ
4
2
Define a circuit, with a symbolic quantum channel:
I
n
[
6
]
:
=
q
c
=
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
{
"
H
"
,
"
C
N
O
T
"
,
Q
u
a
n
t
u
m
C
h
a
n
n
e
l
[
{
"
B
i
t
F
l
i
p
"
,
p
}
,
{
2
}
]
,
{
1
,
2
}
}
]
;
q
c
[
"
D
i
a
g
r
a
m
"
]
O
u
t
[
6
]
=
Find the quantum probabilities:
I
n
[
7
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
[
#
,
A
s
s
u
m
p
t
i
o
n
s
{
0
≤
p
≤
1
}
]
&
/
@
q
c
[
]
[
"
P
r
o
b
a
b
i
l
i
t
i
e
s
"
]
O
u
t
[
7
]
=
|
0
0
〉
1
-
p
,
|
0
1
〉
p
,
|
1
0
〉
0
,
|
1
1
〉
0
Create a list of operators using a Hamiltonian as 3-qubits interacting based on Ising model
H
=
X
1
X
2
+
X
2
X
3
. Generate the 4th order Trotter decomposition, for only 1 step:
I
n
[
8
]
:
=
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
{
"
T
r
o
t
t
e
r
i
z
a
t
i
o
n
"
,
{
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
,
{
1
,
2
}
]
,
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
"
X
"
,
{
2
,
3
}
]
}
,
4
,
1
,
t
}
]
/
/
Q
u
a
n
t
u
m
S
h
o
r
t
c
u
t
O
u
t
[
8
]
=
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
1
-
4
4
-
2
/
3
2
t
,
{
X
1
,
X
2
}
,
R
,
1
-
4
4
-
2
/
3
2
t
,
{
X
2
,
X
3
}
,
R
,
1
-
4
4
-
2
/
3
2
t
,
{
X
2
,
X
3
}
,
R
,
1
-
4
4
-
2
/
3
2
t
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
2
,
X
3
}
,
R
,
t
4
-
2
/
3
2
,
{
X
1
,
X
2
}
Phase estimation circuit of a symbolic unitary:
I
n
[
9
]
:
=
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
{
"
P
h
a
s
e
E
s
t
i
m
a
t
i
o
n
"
,
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
{
"
P
"
,
θ
}
]
,
3
}
]
[
"
D
i
a
g
r
a
m
"
]
O
u
t
[
9
]
=
Composition of circuits:
I
n
[
1
0
]
:
=
q
c
=
Q
u
a
n
t
u
m
M
e
a
s
u
r
e
m
e
n
t
O
p
e
r
a
t
o
r
[
{
1
,
2
}
]
@
*
(
Q
u
a
n
t
u
m
O
p
e
r
a
t
o
r
[
{
"
R
X
"
,
ϕ
}
]
^
2
)
@
*
Q
u
a
n
t
u
m
C
i
r
c
u
i
t
O
p
e
r
a
t
o
r
[
"
M
a
g
i
c
"
]
;
q
c
[
"
D
i
a
g
r
a
m
"
]
O
u
t
[
1
0
]
=
Calculate the quantum probabilities:
I
n
[
1
1
]
:
=
F
u
l
l
S
i
m
p
l
i
f
y
[
#
,
A
s
s
u
m
p
t
i
o
n
s
{
ϕ
∈
R
e
a
l
s
}
]
&
/
@
q
c
[
]
[
"
P
r
o
b
a
b
i
l
i
t
i
e
s
"
]
O
u
t
[
1
1
]
=
0
0
2
C
o
s
[
ϕ
]
2
,
0
1
2
S
i
n
[
ϕ
]
2
,
1
0
2
S
i
n
[
ϕ
]
2
,
1
1
2
C
o
s
[
ϕ
]
2
External Links
QuantumMeasurementOperator
See Also
Wolfram/QuantumFramework
Publisher Information
Contributed by:
Wolfram Research, Quantum Computation Framework Team
