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yaniccd merged 2 commits into from
Aug 11, 2026
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Patch 1 #102

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minor changes in paper.md
danielskatz Aug 11, 2026
1762192
minor changes in paper.bib
danielskatz Aug 11, 2026
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20 changes: 10 additions & 10 deletions paper/paper.bib
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@@ -1,5 +1,5 @@
@article{10.7717/peerj-cs.103,
title = {SymPy: symbolic computing in Python},
title = {SymPy: symbolic computing in {P}ython},
author = {Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and \v{C}ert\'{i}k, Ond\v{r}ej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, Amit and Ivanov, Sergiu and Moore, Jason K. and Singh, Sartaj and Rathnayake, Thilina and Vig, Sean and Granger, Brian E. and Muller, Richard P. and Bonazzi, Francesco and Gupta, Harsh and Vats, Shivam and Johansson, Fredrik and Pedregosa, Fabian and Curry, Matthew J. and Terrel, Andy R. and Rou\v{c}ka, \v{S}t\v{e}p\'{a}n and Saboo, Ashutosh and Fernando, Isuru and Kulal, Sumith and Cimrman, Robert and Scopatz, Anthony},
year = 2017,
month = Jan,
Expand Down Expand Up @@ -30,7 +30,7 @@ @article{bordenave2024strong


@article{cardin2024photon,
title={Photon-number moments and cumulants of Gaussian states},
title={Photon-number moments and cumulants of {G}aussian states},
author={Cardin, Yanic and Quesada, Nicol{\'a}s},
journal={Quantum},
volume={8},
Expand All @@ -55,7 +55,7 @@ @article{collins2003moments


@article{collins2006integration,
title={Integration with respect to the Haar measure on unitary, orthogonal and symplectic group},
title={Integration with respect to the {H}aar measure on unitary, orthogonal and symplectic group},
author={Collins, Beno{\^\i}t and {\'S}niady, Piotr},
journal={Communications in Mathematical Physics},
volume={264},
Expand All @@ -81,7 +81,7 @@ @article{cotler2017chaos


@inproceedings{daigle2025mixed,
title={Mixed symmetries of Sn: immanants in the sampling of U (d) submatrices},
title={Mixed symmetries of Sn: immanants in the sampling of U(d) submatrices},
author={Daigle, Jacob and {de Guise}, Hubert and Welsh, Trevor},
booktitle={Journal of Physics: Conference Series},
volume={3152},
Expand Down Expand Up @@ -113,7 +113,7 @@ @article{duschenes2025moments


@article{fukuda2023symbolically,
title={Symbolically integrating tensor networks over various random tensors by the second version of Python RTNI},
title={Symbolically integrating tensor networks over various random tensors by the second version of {P}ython RTNI},
author={Fukuda, Motohisa},
journal={arXiv preprint arXiv:2309.01167},
year={2023},
Expand Down Expand Up @@ -146,15 +146,15 @@ @book{james1978representation


@book{macdonald1998symmetric,
title={Symmetric functions and Hall polynomials},
title={Symmetric functions and {H}all polynomials},
author={Macdonald, Ian Grant},
year={1998},
publisher={Oxford university press}
}


@article{martinez2024linear,
title={Linear cross-entropy certification of quantum computational advantage in gaussian boson sampling},
title={Linear cross-entropy certification of quantum computational advantage in {G}aussian boson sampling},
author={Mart{\'\i}nez-Cifuentes, Javier and {de Guise}, Hubert and Quesada, Nicol{\'a}s},
journal={PRX Quantum},
volume={5},
Expand All @@ -167,7 +167,7 @@ @article{martinez2024linear


@article{mele2024introduction,
title={Introduction to Haar measure tools in quantum information: A beginner's tutorial},
title={Introduction to {H}aar measure tools in quantum information: A beginner's tutorial},
author={Mele, {Antonio Anna}},
journal={Quantum},
volume={8},
Expand Down Expand Up @@ -196,7 +196,7 @@ @book{nica2006lectures


@misc{OliviaDiMatteo2021,
title={Understanding the Haar measure},
title={Understanding the {H}aar measure},
author={Olivia {Di Matteo}},
year={2021},
month={3},
Expand All @@ -208,7 +208,7 @@ @misc{OliviaDiMatteo2021


@article{pawela2026integrateunitary,
title={IntegrateUnitary.{j}l: A Julia package for symbolic integration over Haar measures},
title={IntegrateUnitary.{j}l: A {J}ulia package for symbolic integration over {H}aar measures},
author={Pawela, {\L}ukasz and Pucha{\l}a, Zbigniew},
journal={arXiv preprint arXiv:2605.23830},
year={2026},
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2 changes: 1 addition & 1 deletion paper/paper.md
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Expand Up @@ -31,7 +31,7 @@ Rather than relying on Monte Carlo simulation, which provides approximate result

Under the hood, Haarpy reduces the computation of integrals over the relevant ensembles to Weingarten calculus.
This field has grown rapidly over the past few decades, following the foundational work of Collins, who introduced the terminology [@collins2003moments; @collins2006integration].
This machinery is exposed through functions such as `weingarten_unitary`, `weingarten_orthogonal` and `weingarten_symplectic` while the associated integrals are accessed through functions such as `haar_integral_unitary`, `haar_integral_orthogonal` and `haar_integral_symplectic`.
This machinery is exposed through functions such as `weingarten_unitary`, `weingarten_orthogonal`, and `weingarten_symplectic`, while the associated integrals are accessed through functions such as `haar_integral_unitary`, `haar_integral_orthogonal`, and `haar_integral_symplectic`.
A full description of Haarpy's functionalities can be found in the library [documentation](https://haarpy.readthedocs.io).

Built on top of the SymPy symbolic engine, Haarpy allows users to retain symbolic parameters and derive general formulas applicable across entire classes of problems [@10.7717/peerj-cs.103].
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