The QuantumComputing package is an environment for performing simulations of a quantum computer in Maple.

Unlike most simulators, Maple can compute with both exact arithmetic (i.e. rational and irrational numbers) and symbolic variables.  

The wave function is printed using an easy-to-understand Dirac-like notation.

The QuantumComputing package is a subpackage of the QuantumChemistry package.

Each command in the QuantumComputing package can be accessed by (1) loading the commands of the QuantumChemistry package the command with(QuantumChemistry) and loading the commands of the QuantumComputing subpackage via with(QuantumComputing) and (2) calling each command as Command(arguments) with appropriate arguments as described in the command's help page.  See the short form for additional details.

Each command in the QuantumComputing package can be accessed by (1) loading the commands of the QuantumChemistry package the command with(QuantumChemistry) and (2) calling each command as either QuantumComputing[Command](arguments) or QuantumComputing:-Command(arguments) with appropriate arguments as described in the command's help page.  

Each command in the QuantumComputing package can be accessed without loading either the QuantumChemistry package or the QuantumComputing subpackage via the following two formats: (1)  QuantumChemistry[QuantumComputing][Command](arguments) or (2) QuantumChemistry:-QuantumComputing:-Command(arguments) with appropriate arguments as described in the command's help page.  See the long form for additional details.    

M. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

D. McMahon, Quantum Computing Explained (John Wiley & Sons, New York, 2007).

W. Scherer, Mathematics of Quantum Computing (Springer, New York, 2019).

G. Benenti, G. Casati, D. Rossini, and G. Strini, Principles of Quantum Computation and Information: A Comprehensive Textbook (World Scientific Publishing Company, London, 2019).

Amira Abbas and Stina Andersson and Abraham Asfaw and Antonio Corcoles and Luciano Bello and Yael Ben-Haim and Mehdi Bozzo-Rey and Sergey Bravyi and Nicholas Bronn and Lauren Capelluto and Almudena Carrera Vazquez and Jack Ceroni and Richard Chen and Albert Frisch and Jay Gambetta and Shelly Garion and Leron Gil and Salvador De La Puente Gonzalez and Francis Harkins and Takashi Imamichi and Pavan Jayasinha and Hwajung Kang and Amir h. Karamlou and Robert Loredo and David McKay and Alberto Maldonado and Antonio Macaluso and Antonio Mezzacapo and Zlatko Minev and Ramis Movassagh and Giacomo Nannicini and Paul Nation and Anna Phan and Marco Pistoia and Arthur Rattew and Joachim Schaefer and Javad Shabani and John Smolin and John Stenger and Kristan Temme and Madeleine Tod and Ellinor Wanzambi and Stephen Wood and James Wootton, Learn Quantum Computation using Qiskit (IBM, Heightstown, New York, 2023). https://qiskit.org/textbook/preface.html

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

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

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

$\mathrm{Uz} ≔ \mathrm{Gate}\left(''Z''\right)\;$

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

$\mathrm{Uz}\,\mathrm{Uy} ≔ \mathrm{Gate}\left(''X''\right)\,\mathrm{Gate}\left(''Y''\right)\;$

$\mathrm{Uz},\mathrm{Uy}≔\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}0& \mathrm{-I}\\ \mathrm{I}& 0\end{array}\right]$

$\mathrm{Uu} ≔ \mathrm{Gate}\left(''U''\,\mathrm{theta}\=\mathrm{theta}\,\mathrm{phi}\=\mathrm{phi}\,\mathrm{lambda}\=\mathrm{lambda}\right)\;$

$\mathrm{Uu}≔\left[\begin{array}{cc}\cos \left(\frac{\mathrm{\theta }}{2}\right)& -{\ⅇ}^{\mathrm{I}\mathrm{\lambda }}\sin \left(\frac{\mathrm{\theta }}{2}\right)\\ {\ⅇ}^{\mathrm{I}\mathrm{\phi }}\sin \left(\frac{\mathrm{\theta }}{2}\right)& {\ⅇ}^{\mathrm{I}\left(\mathrm{\phi }+\mathrm{\lambda }\right)}\cos \left(\frac{\mathrm{\theta }}{2}\right)\end{array}\right]$

$\mathrm{Ucnot} ≔ \mathrm{Gate}\left(''CNOT''\right)\;$

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

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

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

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

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

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

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

$\mathrm{QubitPopulationsPlot}\left(\mathrm{state2}\right)\;$