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QuantumFramework

Tutorials

  • Getting Started

Guides

  • Wolfram Quantum Computation Framework

Tech Notes

  • Diagram
  • Exploring Fundamentals of Quantum Theory
  • Quantum Computation

Symbols

  • QuantumBasis
  • QuantumChannel
  • QuantumCircuitOperator
  • QuantumDistance
  • QuantumEntangledQ
  • QuantumEntanglementMonotone
  • QuantumEvolve
  • QuantumMeasurement
  • QuantumMeasurementOperator
  • QuantumMeasurementSimulation
  • QuantumOperator
  • QuantumPartialTrace
  • QuantumStateEstimate[EXPERIMENTAL]
  • QuantumState
  • QuantumStuff
  • QuantumTensorProduct
  • QuditBasis
  • QuditName
Wolfram`QuantumFramework`
QuantumBasis
​
QuantumBasis
["name"]
represents a named quantum basis
"name"
.
​
​
QuantumBasis
[{"name",d}]
represents a
d
-dimensional version of a named quantum basis
"name"
.
​
​
QuantumBasis
[
name
1

b
1
,
name
2

b
2
,…]
represents a quantum basis with basis elements
b
i
, having names
name
i
.
​
​
QuantumBasis
[{
n
1
,
n
2
,…}]
represents a
n
1
×
n
2
×…
dimensional computational basis of a composite system (many qudits).
​
​
QuantumBasis
[n,m]
represents a
m
n
dimensional computational basis of a composite system (
m
qudits, each one,
n
-dimensional).
​
Details and Options

Examples  
(21)
Basic Examples  
(7)
Create 2-dimensional basis:
In[1]:=
QuantumBasis
[2]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 1
Dimension: 2
​

Note with no input, the basis is automatically set as 2D, bu default
In[2]:=
QuantumBasis
[2]
QuantumBasis
[]
Out[2]=
True
​
Create 3-dimensional basis:
In[1]:=
QuantumBasis
[3]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 1
Dimension: 3
​

​
Create a 2×2×2 dimensional basis (three qubits):
In[1]:=
QuantumBasis
[2,3]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 3
Dimension: 8
​

In[2]:=
%["Dimensions"]
Out[2]=
{2,2,2}
​
Create composite basis of two 2 and 3-dimensional qudits:
In[1]:=
QuantumBasis
[{2,3}]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 2
Dimension: 6
​

In[2]:=
%["Dimensions"]
Out[2]=
{2,3}
​
Create a 2-dimensional basis using explicit element representations:
In[1]:=
QuantumBasis
[0{1,2},1{0,1}]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 1
Dimension: 2
​

​
Construct a Pauli-Y basis for 2 qubits:
In[1]:=
basis=
QuantumBasis
["PauliY"]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 1
Dimension: 2
​

Return a matrix representation:
In[2]:=
Normal/@basis["ElementAssociation"]
Out[2]=

ψ
y
-


2
,
1
2
,
ψ
y
+
-

2
,
1
2

​
Represent the Bell basis for a single qubit (default):
In[1]:=
basis=
QuantumBasis
["Bell"]
Out[1]=
QuantumBasis
Picture: Schrödinger
Rank: 1
Dimension: 4
​

Return its element names:
In[2]:=
basis["Names"]
Out[2]=
{|
-
Φ
〉,|
+
Φ
〉,|
-
Ψ
〉,|
+
Ψ
〉}
Scope  
(8)

Generalizations & Extensions  
(1)

Applications  
(1)

Properties & Relations  
(4)

SeeAlso
QuantumState
 
▪
QuantumTensorProduct
 
▪
QuantumOperator
RelatedGuides
▪
Wolfram Quantum Computation Framework
""

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