The MeasureState command accepts a circuit as a list of equations and a quantum state.  

In the circuit the left side of an equation indicates the qubit or qubits on which the operator acts and the right side provides the operator itself.  When the left side of an equation is a single qubit, it should be expressed as an integer, but when the left side represents two or more qubits, it should be expressed as a list of integers.  The right side of an equation can be generated by the Gate command or provided by the user.

The quantum state can be expressed in Dirac notation (polynom) or as a multidimensional Array (Array).    

The MeasureState command returns the expectation value of the circuit, which is a product of the operators in the list, with respect to the given quantum state.

The optional boolean keyword dirac determines whether the output state is returned in Dirac notation (true) or Array notation (false).

In Dirac notation the number of qubits is represented by the number of indices on the wave function symbol; in Array notation the number of qubits is represented by the number of dimensions of the Array.

The two states of each qubit are denoted as 0 and 1 in Dirac notation; they are represented by the range 1..2 of each dimension in Array notation.

$\mathrm{with}\left(\mathrm{QuantumChemistry}\right)\:$

$\mathrm{with}\left(\mathrm{QuantumComputing}\right)\;$

$\left[\mathrm{ConvertDirac}\,\mathrm{Gate}\,\mathrm{InitialState}\,\mathrm{MeasureState}\,\mathrm{PrepareState}\,\mathrm{QubitPopulations}\,\mathrm{QubitPopulationsPlot}\right]$

$\mathrm{state0} ≔ \mathrm{InitialState}\left(4\right)\;$

$\mathrm{state0}≔{\mathrm{\Psi }}_{0,0,0,0}$

$\mathrm{circuit} ≔ \left[1\= \mathrm{Gate}\left(''H''\right)\,\mathrm{seq}\left(\left[i\,i\+1\right]\=\mathrm{Gate}\left(''CNOT''\right)\, i\=1..3\right)\right]\;$

$\mathrm{circuit}≔\left[1=\left[\begin{array}{cc}\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}\\ \frac{\sqrt{2}}{2}& -\frac{\sqrt{2}}{2}\end{array}\right]\,\left[1\,2\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\end{array}\right]\,\left[2\,3\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\end{array}\right]\,\left[3\,4\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\end{array}\right]\right]$

$\mathrm{state2} ≔ \mathrm{PrepareState}\left(\mathrm{circuit}\,\mathrm{state0}\right)\;$

$\mathrm{state2}≔\frac{\sqrt{2}{\mathrm{\Psi }}_{0,0,0,0}}{2}+\frac{\sqrt{2}{\mathrm{\Psi }}_{1,1,1,1}}{2}$

$\mathrm{UpOperator} ≔ \frac{\left(\mathrm{Gate}\left(''I''\right)-\mathrm{Gate}\left(''Z''\right)\right)}{2}\;$

$\mathrm{UpOperator}≔\left[\begin{array}{cc}0& 0\\ 0& 1\end{array}\right]$

$\mathrm{MeasureState}\left(\left[1\=\mathrm{UpOperator}\right]\,\mathrm{state2}\right)\;$

$\frac{1}{2}$