Computer Science
Physics
Quantum Computation

Bit-Flip Noise Effect

Compute the effect of an incoherent bit-flip noise channel on the expected value of a quantum operator

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A BitFlip quantum channel performs a bit-flip operation on a qubit with probability "p", and with probability "1-p" the identity operator is applied. The resulting state after the execution of the channel is always a random mixed state because it simulates entanglement with the environment.

Install the Quantum Framework paclet:

In[1]:=

PacletInstall["Wolfram/QuantumFramework"]

Load the paclet:

In[2]:=

Needs["Wolfram`QuantumFramework`"]

Compute the matrix form of the BitFlip Kraus operators:

In[3]:=

Thread[{"

","

"}MatrixForm/@QuantumChannel[{"BitFlip",p}]["Tensor"]]

Out[3]=





1-p	0
0	1-p



0	p
p	0



Find the expected value of



operator without noise (use eigenvalue multiplication in QuantumMeasurementOperator):

In[4]:=

qc=QuantumCircuitOperator[{"H"1,"CNOT"{1,2},QuantumMeasurementOperator["PauliZ"{1,-1,-1,1},{1,2}]}];qc[]["Mean"]

Out[4]=

Define the noisy circuit and get the diagram (define p as the circuit parameter):

In[5]:=

qc=QuantumCircuitOperator "H"1,"CNOT"{1,2},QuantumChannel[{"BitFlip",p},{1,2}],QuantumMeasurementOperator["PauliZ"{1,-1,-1,1},{1,2}],"Parameters"{p};qc["Diagram",ImageSizeSmall]

Out[5]=

Calculate the symbolic expected value:

In[6]:=

noisyMean=qc[]["Mean"]

Out[6]=

2Abs[(1-p)p]

2Abs[(1-p)p]+2Abs

(1-p)(1-Conjugate[p])+

pConjugate[p]

2Abs

(1-p)(1-Conjugate[p])+

pConjugate[p]

2Abs[(1-p)p]+2Abs

(1-p)(1-Conjugate[p])+

pConjugate[p]

Plot the mean with respect to the BitFlip parameter p for the state 

〉:

In[7]:=

ShowPlot[noisyMean,{p,0,0.5}],



Out[7]=

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Citation:
- Citation: Arrazola,J.(2021, Feb 21) Noisy Circuits. PennyLane Demos

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Contributed by: Wolfram Research (Quantum Computation Framework Team)

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Bit-Flip Noise Effect

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