ListPlot[QuantumMeasurementOperator[{1,2,3,4}][QuantumState[{"RandomPure",4}]]["Probabilities"],
MeshFunctions->{Log[-Log[1 - #2]]&},Mesh->{3},MeshStyle -> {Directive[PointSize[Medium]]},Joined -> True]
Phenomenal overview. That is a good question; it depends on how you define example circuit; anyhow there are example circuits for Variational Quantum Algorithms or Variational Quantum Eigensolvers.
