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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
  • QuantumState
  • QuantumTensorProduct
  • QuditBasis
  • QuditName
Wolfram`QuantumFramework`
QuantumStateEstimate
[
EXPERIMENTAL
]
​
QuantumStateEstimate[
qmo
1

result
1
,
qmo
2

result
2
,...]
represents a quantum state estimate with quantum measurement operators
qmo
i
, amnd the experimental (or simulated) results
result
i
.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Define a 2D random mixed state:
In[1]:=
state=
QuantumState
["RandomMixed"];
Simulate some measurement results for different measurement, given the above state:
In[2]:=
result=
QuantumMeasurementSimulation
state,
QuantumMeasurementOperator
/@{"X","Y","Z"},100
Out[2]=
QuantumMeasurementOperator
Measurement Type: Projection
Target: {1}
Dimension: 2→2
Qudits: 1→1
{51,49},QuantumMeasurementOperator
Measurement Type: Projection
Target: {1}
Dimension: 2→2
Qudits: 1→1
{4,96},QuantumMeasurementOperator
Measurement Type: Projection
Target: {1}
Dimension: 2→2
Qudits: 1→1
{63,37}
Find the corresponding quantum state estimation
In[3]:=
estimation=
QuantumStateEstimate
[result]
Out[3]=
QuantumStateEstimation
Dimension: 2
Possible Outcomes: 6
Invertible: True
Counts: 100

Generate 100 states using the corresponding Bayesian sampling function:
In[4]:=
samples=estimation["BayesianSampler"][100];
Show histogram of fidelity wrt the original quantum state:
In[5]:=
Histogram
QuantumDistance
[#,state,"Fidelity"]&/@samples
Out[5]=
SeeAlso
QuantumState
 
▪
QuantumBasis
 
▪
QuantumMeasurementOperator
 
▪
QuantumCircuitOperator
TechNotes
▪
QuantumStateEstimate[
…
]
uses measurement results to estimate properties of the preparation, including the system's quantum state. It checks if the measurements provided form a complete set for quantum state reconstruction, and then it performs maximum likelihood state estimation, and returns a Bayesian sampling function. The sampling function generates quantum states distributed according to the measurement results, with a prior given by the Bures metric. Under the hood, it uses a Metropolis-Hastings algorithm where the random walk is implemented with matrix operations, rather than the usual random steps. The sampled states can be used to get Bayesian distributions of any parameters of the measured system. This includes the Bayesian mean quantum state.
RelatedGuides
▪
Wolfram Quantum Computation Framework
RelatedLinks
Wolfram Winter School 2023: Quantum State Estimation
""

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