Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumStateEstimate [ ]  |
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QuantumStateEstimate[…]
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The following properties are supported:
"BayesianSampler" | the corresponding Bayesian sampling function |
Examples
(3)
Basic Examples
(2)
Define a random 2-qubit mixed state:
In[1]:=
state=
["RandomMixed"[2]];
 | QuantumState |
Simulate some measurement results for different measurement, given the above state:
In[2]:=
result=
state,
/@Tuples[{"X","Y","Z"},2],100
 | QuantumMeasurementSimulation |
 | QuantumMeasurementOperator |
Out[2]=
QuantumMeasurementOperator
{36,11,20,33},QuantumMeasurementOperator
{33,21,31,15},QuantumMeasurementOperator
{26,23,28,23},QuantumMeasurementOperator
{52,16,8,24},QuantumMeasurementOperator
{53,22,10,15},QuantumMeasurementOperator
{30,27,28,15},QuantumMeasurementOperator
{31,30,31,8},QuantumMeasurementOperator
{23,31,31,15},QuantumMeasurementOperator
{35,35,23,7}
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Find the corresponding quantum state estimation:
In[3]:=
estimation=
[result]
| QuantumStateEstimate |
Out[3]=
QuantumStateEstimation
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See the list of available properties:
In[4]:=
estimation["Properties"]
Out[4]=
{Invertible,PhysicalInversion,InversionState,MaximumLikelihoodState,MaximumLikelihoodAcceptanceRatio,MaximumLikelihoodConvergence,MaximumLikelihoodConvergenceStepSize,BayesianAcceptanceRatio,BayesianSampler,TotalCounts,CountsPerMeasurement,Dimension,MetropolisStepSize,MeasurementOutcomes}
Generate 100 states using the corresponding Bayesian sampling function:
In[5]:=
samples=estimation["BayesianSampler"][100];
Show histogram of fidelity w.r.t. the original quantum state:
In[6]:=
Histogram
[#,state,"Fidelity"]&/@samples
| QuantumSimilarity |
Out[6]=
Define the state:
In[1]:=
truth=
["BlochVector"[{0.1,0.15,0.7}]];
| QuantumState |
Define the measurement operators:
In[2]:=
ops=
/@{"X","Y","Z"};
| QuantumMeasurementOperator |
Estimate the state sampled by the "BayesianSampler", the standard deviation of each Bloch coordinate for the samples, and the fidelity of the maximum likelihood state, while varying the number of measurement counts:
In[3]:=
TableWithest=
[truth,ops,n],n,StandardDeviation[(#1["BlochCartesianCoordinates"]&)/@est["BayesianSampler"][200,"Burn"50]],
[truth,est["MaximumLikelihoodState"]],{n,{20,100,1000,10000}}//Column
 | QuantumStateEstimate |
| QuantumMeasurementSimulation |
| QuantumSimilarity |
Out[3]=
{20,{0.143087,0.19357,0.105343},0.921012} |
{100,{0.0728716,0.0989784,0.0684391},0.995973} |
{1000,{0.0310168,0.0250211,0.0187719},0.99954} |
{10000,{0.00912016,0.00772599,0.00558625},0.99999} |
Scope
(1)
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""