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QuantumFramework

Tutorials

  • Getting Started

Guides

  • Wolfram Quantum Computation Framework

Tech Notes

  • Bell's Theorem
  • Circuit Diagram
  • Exploring Fundamentals of Quantum Theory
  • Quantum object abstraction
  • Tensor Network

Symbols

  • QuantumBasis
  • QuantumChannel
  • QuantumCircuitMultiwayGraph [EXPERIMENTAL]
  • QuantumCircuitOperator
  • QuantumDistance
  • QuantumEntangledQ
  • QuantumEntanglementMonotone
  • QuantumEvolve
  • QuantumMeasurement
  • QuantumMeasurementOperator
  • QuantumMeasurementSimulation
  • QuantumMPS [EXPERIMENTAL]
  • QuantumOperator
  • QuantumPartialTrace
  • QuantumShortcut [EXPERIMENTAL]
  • QuantumStateEstimate [EXPERIMENTAL]
  • QuantumState
  • QuantumTensorProduct
  • QuantumWignerMICTransform [EXPERIMENTAL]
  • QuantumWignerTransform [EXPERIMENTAL]
  • QuditBasis
  • QuditName
Wolfram`QuantumFramework`
QuantumOperator
​
QuantumOperator
[rep,order,qb]
represents an operator with matrix/tensor representation
rep
that acts on a state at the qubits indexed in
order
, in the quantum basis
qb
.
​
​
QuantumOperator
["name",order,qb]
represents the named operator
"name"
that acts on a state at the qubits indexed in
order
, in the discrete quantum basis
qb
.
​
​
QuantumOperator
[qo,basis]
changes the basis of the
QuantumOperator
qo
to the quantum basis
qb
.
​
Details and Options

Examples  
(61)
Basic Examples  
(6)
Create an operator, given a matrix, with
order=3
, in the Pauli X basis:
In[1]:=
QuantumOperator
[{{1,-1},{1,1}},{3},"X"]
Out[1]=
QuantumOperator
Picture: Schrödinger
Arity: 1
Dimension: 2→2
Qudits: 1→1

​
Create an angular-momentum operator
J
z
with
j=3/2
:
In[1]:=
jz=
QuantumOperator
[{"JZ",3/2}]
Out[1]=
QuantumOperator
Picture: Schrödinger
Arity: 1
Dimension: 4→4
Qudits: 1→1

In[2]:=
jz["Formula"]
Out[2]=
3
2
|0〉〈0|+
1
2
|1〉〈1|-
1
2
|2〉〈2|-
3
2
|3〉〈3|
​
Create a generalized Pauli X in the 3 dimension:
In[1]:=
QuantumOperator
["X"[3]]
Out[1]=
QuantumOperator
Picture: Schrödinger
Arity: 1
Dimension: 3→3
Qudits: 1→1

​
Create a CNOT gate, with qubit-3 as the control and qubit-4 as the target:
In[1]:=
QuantumOperator
["CNOT",{3,4}]
Out[1]=
QuantumOperator
Picture: Schrödinger
Arity: 2
Dimension: 4→4
Qudits: 2→2

​
Controlled operators, for example acting "X" on target qubits, with many controlled-0 and 1 qubits:
In[1]:=
QuantumOperator
[{"C","X"{1,3},{2},{4,5}}]["CircuitDiagram"]
Out[1]=
​
Create a quantum Multiplexer:
In[1]:=
QuantumOperator
[{"Multiplexer","Z","H","X"}]
Out[1]=
QuantumOperator
Picture: Schrödinger
Arity: 1
Dimension: 6→6
Qudits: 1→1

Represent its circuit diagram:
In[2]:=
QuantumCircuitOperator
[{"Multiplexer","Z","H","X"}]["Diagram"]
Out[2]=
Scope  
(54)

Generalizations & Extensions  
(1)

SeeAlso
QuantumState
 
▪
QuantumBasis
 
▪
QuantumMeasurementOperator
 
▪
QuantumChannel
RelatedGuides
▪
Wolfram Quantum Computation Framework
""

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