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Computer Science
Mathematics
Physics
Quantum Computation
Visualization of Quantum Measurement Probabilities
Visualize measurement results
Example Notebook
Open in Cloud
Download Notebook
Install and load the QuantumFramework paclet:
I
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P
a
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n
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a
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[
"
W
o
l
f
r
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/
Q
u
a
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t
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m
F
r
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]
N
e
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d
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`
Q
u
a
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w
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"
]
Given a random pure state, measure qubit-1 in the computational basis:
I
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[
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[
"
R
a
n
d
o
m
P
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]
]
O
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Q
u
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M
e
a
s
u
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m
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T
a
r
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e
t
:
{
1
}
M
e
a
s
u
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m
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n
t
O
u
t
c
o
m
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s
:
2
Plot measurement probabilities:
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a
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P
r
o
b
a
b
i
l
i
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y
P
l
o
t
"
]
O
u
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3
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=
Measure a 3D-qubit in its computational basis:
I
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:
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m
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a
=
Q
u
a
n
t
u
m
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e
a
s
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m
e
n
t
O
p
e
r
a
t
o
r
[
Q
u
a
n
t
u
m
B
a
s
i
s
[
3
]
]
[
Q
u
a
n
t
u
m
S
t
a
t
e
[
"
R
a
n
d
o
m
P
u
r
e
"
,
{
3
}
]
]
O
u
t
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4
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Q
u
a
n
t
u
m
M
e
a
s
u
r
e
m
e
n
t
T
a
r
g
e
t
:
{
1
}
M
e
a
s
u
r
e
m
e
n
t
O
u
t
c
o
m
e
s
:
3
Plot measurement probabilities:
I
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:
=
m
e
a
[
"
P
r
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b
a
b
i
l
i
t
y
P
l
o
t
"
]
O
u
t
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5
]
=
Given a random pure state, measure qubit-1 in Pauli-X basis:
I
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:
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m
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a
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p
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r
a
t
o
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[
"
X
"
]
[
Q
u
a
n
t
u
m
S
t
a
t
e
[
"
R
a
n
d
o
m
P
u
r
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"
]
]
O
u
t
[
6
]
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Q
u
a
n
t
u
m
M
e
a
s
u
r
e
m
e
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T
a
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g
e
t
:
{
1
}
M
e
a
s
u
r
e
m
e
n
t
O
u
t
c
o
m
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s
:
2
Show measurement probabilities:
I
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m
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a
[
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P
r
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b
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]
O
u
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7
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=
ψ
x
-
0
.
8
5
4
6
6
8
,
ψ
x
+
0
.
1
4
5
3
3
2
Plot measurement probabilities for measuring a 2x3 composite system in computational basis:
I
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[
8
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:
=
Q
u
a
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t
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m
M
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a
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a
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o
r
[
Q
u
a
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t
u
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B
a
s
i
s
[
{
2
,
3
}
]
]
[
Q
u
a
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t
u
m
S
t
a
t
e
[
"
R
a
n
d
o
m
P
u
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,
{
2
,
3
}
]
]
[
"
P
r
o
b
a
b
i
l
i
t
y
P
l
o
t
"
]
O
u
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8
]
=
Define a random pure state for 2-qubits:
I
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:
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ψ
=
Q
u
a
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u
m
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t
a
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[
{
"
R
a
n
d
o
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P
u
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"
,
2
}
]
O
u
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[
9
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=
Q
u
a
n
t
u
m
S
t
a
t
e
P
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r
e
s
t
a
t
e
Q
u
d
i
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:
2
T
y
p
e
:
V
e
c
t
o
r
D
i
m
e
n
s
i
o
n
:
4
P
i
c
t
u
r
e
:
S
c
h
r
ö
d
i
n
g
e
r
Find measurement probabilities, with and without a bit-flip noise channel with the probability 0.3:
I
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1
0
]
:
=
m
1
=
Q
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a
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m
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r
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o
r
[
{
1
,
2
}
]
[
ψ
]
;
m
2
=
Q
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m
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[
{
1
,
2
}
]
[
Q
u
a
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t
u
m
C
h
a
n
n
e
l
[
{
"
B
i
t
F
l
i
p
"
,
.
3
}
]
[
ψ
]
]
;
Compare measurement results:
I
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1
1
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=
B
a
r
C
h
a
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t
T
r
a
n
s
p
o
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e
[
V
a
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/
@
{
m
1
[
"
P
r
o
b
a
b
i
l
i
t
i
e
s
"
]
,
m
2
[
"
P
r
o
b
a
b
i
l
i
t
i
e
s
"
]
}
]
,
O
u
t
[
1
1
]
=
External Links
QuantumState
QuantumMeasurementOperator
See Also
Wolfram/QuantumFramework
Publisher Information
Contributed by:
Wolfram Research, Quantum Computation Framework Team
