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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
  • QuantumMeasurement
  • QuantumMeasurementOperator
  • QuantumMeasurementSimulation
  • QuantumOperator
  • QuantumPartialTrace
  • QuantumStateEstimate
  • QuantumState
  • QuantumTensorProduct
  • QuditBasis
  • QuditName
Wolfram`QuantumFramework`
QuantumChannel
​
QuantumChannel[ko,order,qb]
represents a quantum channel with Kraus operators
ko
, in basis
qb
, to be applied onto the qubits indexed in
order
.
​
​
QuantumChannel[name,par]
represents a the named quantum channel with name
name
, and potential parameters specified by
par
.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
Define a quantum channel
In[1]:=
ops=Table
QuantumOperator
["RandomUnitary"]Sqrt[4],4;​​channel=
QuantumChannel
[ops]
Out[1]=
QuantumChannel
Picture: Schrödinger
Arity: 1
Dimension: 2
Qudits: 1

Apply the channel on a random mixed state:
In[2]:=
channel
QuantumState
["RandomMixed"]
Out[2]=
QuantumState
StateType: Matrix
Qudits: 1
Type: Mixed
Dimension: 2
Picture: Schrödinger
​

Scope  
(1)

SeeAlso
QuantumState
 
▪
QuantumBasis
 
▪
QuantumMeasurementOperator
TechNotes
▪
The bit-flip channel is represented by the quantum channel
QuantumChannel[{
p
QuantumOperator["X"],
1-p
QuantumOperator["I"]}]
. In this channel, a qubit undergoes a bit-flip operation with probability p and remains unchanged with probability 1 - p.
▪
The phase-flip channel is represented by the quantum channel
QuantumChannel[{
p
QuantumOperator["Z"],
1-p
QuantumOperator["I"]}]
. In this channel, a qubit undergoes a phase-flip operation with probability p and remains unchanged with probability 1 - p.
▪
The bit-phase-flip channel is represented by the quantum channel
QuantumChannel[{
p
QuantumOperator["Y"],
1-p
QuantumOperator["I"]}]
. In this channel, a qubit undergoes a combined bit and phase-flip operation with probability p and remains unchanged with probability 1 - p.
▪
The depolarizing channel is represented by the quantum channel
QuantumChannel[{
p/4
QuantumOperator["X"],
p/4
QuantumOperator["Y"],
p/4
QuantumOperator["Z"],
1-3p/4
QuantumOperator["I"]}]
. In this channel, a qubit undergoes a random Pauli operation (X, Y, or Z) with equal probability p/4 or remains unchanged with probability 1 - 3p/4.
▪
The amplitude damping channel is represented by the quantum channel
QuantumChannel[{QuantumOperator[{{1,0},{0,
1-γ
}}],QuantumOperator[{{0,
γ
},{0,0}}]}]
. This channel models the energy relaxation of a qubit, where γ is the damping rate.
▪
The generalized amplitude damping channel is represented by the quantum channel
QuantumChannel[{
p
QuantumOperator[{{1,0},{0,
1-γ
}}],
p
QuantumOperator[{{0,
γ
},{0,0}}],
1-p
QuantumOperator[{{
1-γ
,0},{0,1}}],
1-p
QuantumOperator[{{0,0},{
γ
,0}}]}]
. This channel models the energy relaxation of a qubit in the presence of a thermal environment, where p is the probability of the qubit being excited and γ is the damping rate.
▪
The phase damping channel is represented by the quantum channel
QuantumChannel[{QuantumOperator[{{1,0},{0,
1-λ
}}],QuantumOperator[{{0,0},{0,
λ
}}]}]
. This channel models the dephasing of a qubit, where λ is the dephasing rate.
RelatedGuides
▪
Wolfram Quantum Computation Framework
""

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