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21 changes: 21 additions & 0 deletions bbt.bib
Original file line number Diff line number Diff line change
Expand Up @@ -446,6 +446,27 @@ @article{Cao2025
bibsource = qplbib
}

@article{Carette2024,
author = {Carette, Jacques and Heunen, Chris and Kaarsgaard, Robin and Sabry, Amr},
title = {With a Few Square Roots, Quantum Computing Is as Easy as Pi},
year = {2024},
publisher = acm,
address = {New York, NY, USA},
volume = {8},
number = {POPL},
doi = {10.1145/3632861},
abstract = {Rig groupoids provide a semantic model of $\Pi$, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps and three equations about them results in a model of quantum computing that is computationally universal and equationally sound and complete for a variety of gate sets. The first map corresponds to an 8th root of the identity morphism on the unit $1$. The second map corresponds to a square root of the symmetry on $1+1$. As square roots are generally not unique and can sometimes even be trivial, the maps are constrained to satisfy a nondegeneracy axiom, which we relate to the Euler decomposition of the Hadamard gate. The semantic construction is turned into an extension of $\Pi$, called $\sqrt{\Pi}$, that is a computationally universal quantum programming language equipped with an equational theory that is sound and complete with respect to the Clifford gate set, the standard gate set of Clifford+T restricted to $\leq 2$ qubits, and the computationally universal Gaussian Clifford+T gate set.},
journal = pacmpl,
month = jan,
eid = {19},
pages = {546--574},
numpages = {29},
keywords = {quantum programming language, reversible computing, rig category, unitary quantum computing},
webnote = {POPL '24},
bibsource = qplbib
}


@article{Carette2025,
author = {Carette, Jacques and Heunen, Chris and Kaarsgaard, Robin and Sabry, Amr},
title = {How to Bake a Quantum Π},
Expand Down
17 changes: 17 additions & 0 deletions biblatex.bib
Original file line number Diff line number Diff line change
Expand Up @@ -408,6 +408,23 @@ @article{Cao2025
bibsource = qplbib
}

@article{Carette2024,
author = {Carette, Jacques and Heunen, Chris and Kaarsgaard, Robin and Sabry, Amr},
title = {With a Few Square Roots, Quantum Computing Is as Easy as Pi},
year = {2024},
volume = {8},
number = {POPL},
doi = {10.1145/3632861},
abstract = {Rig groupoids provide a semantic model of $\Pi$, a universal classical reversible programming language over finite types. We prove that extending rig groupoids with just two maps and three equations about them results in a model of quantum computing that is computationally universal and equationally sound and complete for a variety of gate sets. The first map corresponds to an 8th root of the identity morphism on the unit $1$. The second map corresponds to a square root of the symmetry on $1+1$. As square roots are generally not unique and can sometimes even be trivial, the maps are constrained to satisfy a nondegeneracy axiom, which we relate to the Euler decomposition of the Hadamard gate. The semantic construction is turned into an extension of $\Pi$, called $\sqrt{\Pi}$, that is a computationally universal quantum programming language equipped with an equational theory that is sound and complete with respect to the Clifford gate set, the standard gate set of Clifford+T restricted to $\leq 2$ qubits, and the computationally universal Gaussian Clifford+T gate set.},
journaltitle = pacmpl,
month = jan,
eid = {19},
keywords = {quantum programming language, reversible computing, rig category, unitary quantum computing},
webnote = {POPL '24},
bibsource = qplbib
}


@article{Carette2025,
author = {Carette, Jacques and Heunen, Chris and Kaarsgaard, Robin and Sabry, Amr},
title = {How to Bake a Quantum Π},
Expand Down
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