The ConvertDirac command converts a quantum state between Dirac notation and an Array.  If the state is given in Dirac notation, it is converted to an Array; if the state is given as an Array, it is converted to Dirac notation.

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.

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

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

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

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

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

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

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

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

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

$\mathrm{state3} ≔ \mathrm{ConvertDirac}\left(\mathrm{state2}\right)\;$

$\mathrm{state4} ≔ \mathrm{ConvertDirac}\left(\mathrm{state3}\right)\;$

$\mathrm{state4}≔\frac{\sqrt{2}{\mathrm{\Psi }}_{0,0,0,0}}{2}+\frac{\sqrt{2}{\mathrm{\Psi }}_{1,1,1,1}}{2}$