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% Author: Théodore CHAPUIS-CHKAIBAN
@article{sidford2,
author = {AmirMahdi Ahmadinejad and
Arun Jambulapati and
Amin Saberi and
Aaron Sidford},
title = {Perron-Frobenius Theory in Nearly Linear Time: Positive Eigenvectors,
M-matrices, Graph Kernels, and Other Applications},
journal = {CoRR},
volume = {abs/1810.02348},
year = {2018},
url = {http://arxiv.org/abs/1810.02348},
eprinttype = {arXiv},
eprint = {1810.02348},
timestamp = {Tue, 30 Oct 2018 10:49:09 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1810-02348.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{sidford,
author = {Michael B. Cohen and
Jonathan A. Kelner and
John Peebles and
Richard Peng and
Aaron Sidford and
Adrian Vladu},
title = {Faster Algorithms for Computing the Stationary Distribution, Simulating
Random Walks, and More},
journal = {CoRR},
volume = {abs/1608.03270},
year = {2016},
url = {http://arxiv.org/abs/1608.03270},
eprinttype = {arXiv},
eprint = {1608.03270},
timestamp = {Mon, 13 Aug 2018 16:48:46 +0200},
biburl = {https://dblp.org/rec/journals/corr/CohenKPPSV16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{low_chuang_2017,
title = {Optimal Hamiltonian Simulation by Quantum Signal Processing},
author = {Low, Guang Hao and Chuang, Isaac L.},
journal = {Phys. Rev. Lett.},
volume = {118},
issue = {1},
pages = {010501},
numpages = {5},
year = {2017},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.118.010501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.118.010501}
}
@article{ortega_frossard_kovacevic_moura_vandergheynst_2018, title={Graph Signal Processing: Overview, Challenges, and Applications}, volume=106, DOI={10.1109/jproc.2018.2820126}, number=5, journal={Proceedings of the IEEE}, author={Ortega, Antonio and Frossard, Pascal and Kovacevic, Jelena and Moura, Jose M. F. and Vandergheynst, Pierre}, year=2018, pages={808–828}}
@article{shuman_narang_frossard_ortega_vandergheynst_2013, title={The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains}, volume=30, DOI={10.1109/msp.2012.2235192}, number=3, journal={IEEE Signal Processing Magazine}, author={Shuman, D. I. and Narang, S. K. and Frossard, P. and Ortega, A. and Vandergheynst, P.}, year=2013, pages={83–98}}
@article{sandryhaila_moura_2014, title={Discrete Signal Processing on Graphs: Frequency Analysis}, volume={62}, DOI={10.1109/tsp.2014.2321121}, number={12}, journal={IEEE Transactions on Signal Processing}, author={Sandryhaila, Aliaksei and Moura, Jose M. F.}, year={2014}, pages={3042–3054}}
@article{Low_2019,
title={Hamiltonian Simulation by Qubitization},
volume={3},
ISSN={2521-327X},
url={http://dx.doi.org/10.22331/q-2019-07-12-163},
DOI={10.22331/q-2019-07-12-163},
journal={Quantum},
publisher={Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften},
author={Low, Guang Hao and Chuang, Isaac L.},
year={2019},
month={Jul},
pages={163}
}
@article{eldar_oppenheim_2002, title={Quantum signal processing}, volume={19}, DOI={10.1109/msp.2002.1043298}, number={6}, journal={IEEE Signal Processing Magazine}, author={Eldar, Y.c. and Oppenheim, A.v.}, year={2002}, pages={12–32}}
@article{brassard_hoyer_mosca_tapp_2002, title={Quantum amplitude amplification and estimation}, DOI={10.1090/conm/305/05215}, journal={Contemporary Mathematics Quantum Computation and Information}, author={Brassard, Gilles and Høyer, Peter and Mosca, Michele and Tapp, Alain}, year={2002}, pages={53–74}}
@article{Krovi_2015,
title={Quantum Walks Can Find a Marked Element on Any Graph},
volume={74},
ISSN={1432-0541},
url={http://dx.doi.org/10.1007/s00453-015-9979-8},
DOI={10.1007/s00453-015-9979-8},
number={2},
journal={Algorithmica},
publisher={Springer Science and Business Media LLC},
author={Krovi, Hari and Magniez, Frédéric and Ozols, Maris and Roland, Jérémie},
year={2015},
month={Mar},
pages={851–907}
}
@article{Magniez_2011,
title={Search via Quantum Walk},
volume={40},
ISSN={1095-7111},
url={http://dx.doi.org/10.1137/090745854},
DOI={10.1137/090745854},
number={1},
journal={SIAM Journal on Computing},
publisher={Society for Industrial & Applied Mathematics (SIAM)},
author={Magniez, Frédéric and Nayak, Ashwin and Roland, Jérémie and Santha, Miklos},
year={2011},
month={Jan},
pages={142–164}
}
@misc{qiskit_hhl, title={Solving Linear Systems of Equations using HHL}, url={https://qiskit.org/textbook/ch-applications/hhl_tutorial.html}, journal={Qiskit}, publisher={Data 100 at UC Berkeley}, author={Team, The Qiskit}, year={2021}, month={Aug}}
@article{Pan_2014,
title={Experimental realization of quantum algorithm for solving linear systems of equations},
volume={89},
ISSN={1094-1622},
url={http://dx.doi.org/10.1103/PhysRevA.89.022313},
DOI={10.1103/physreva.89.022313},
number={2},
journal={Physical Review A},
publisher={American Physical Society (APS)},
author={Pan, Jian and Cao, Yudong and Yao, Xiwei and Li, Zhaokai and Ju, Chenyong and Chen, Hongwei and Peng, Xinhua and Kais, Sabre and Du, Jiangfeng},
year={2014},
month={Feb}
}
@article{Clader_2013,
title={Preconditioned Quantum Linear System Algorithm},
volume={110},
ISSN={1079-7114},
url={http://dx.doi.org/10.1103/PhysRevLett.110.250504},
DOI={10.1103/physrevlett.110.250504},
number={25},
journal={Physical Review Letters},
publisher={American Physical Society (APS)},
author={Clader, B. D. and Jacobs, B. C. and Sprouse, C. R.},
year={2013},
month={Jun}
}
@article{Zhao_2019,
title={Bayesian deep learning on a quantum computer},
volume={1},
ISSN={2524-4914},
url={http://dx.doi.org/10.1007/s42484-019-00004-7},
DOI={10.1007/s42484-019-00004-7},
number={1-2},
journal={Quantum Machine Intelligence},
publisher={Springer Science and Business Media LLC},
author={Zhao, Zhikuan and Pozas-Kerstjens, Alejandro and Rebentrost, Patrick and Wittek, Peter},
year={2019},
month={May},
pages={41–51}
}
@article{Harrow_2009,
title={Quantum Algorithm for Linear Systems of Equations},
volume={103},
ISSN={1079-7114},
url={http://dx.doi.org/10.1103/PhysRevLett.103.150502},
DOI={10.1103/physrevlett.103.150502},
number={15},
journal={Physical Review Letters},
publisher={American Physical Society (APS)},
author={Harrow, Aram W. and Hassidim, Avinatan and Lloyd, Seth},
year={2009},
month={Oct}
}
@article{du_lei_qin_lu_peng_2011, title={Search via Quantum Walk}, DOI={10.5772/15814}, journal={Search Algorithms and Applications}, author={Du, Jiangfeng and Lei, Chao and Qin, Gan and Lu, Dawei and Peng, Xinhua}, year={2011}}
@article{duan_yuan_liu_li_2018, title={Efficient quantum circuit for singular-value thresholding}, volume={98}, DOI={10.1103/physreva.98.012308}, number={1}, journal={Physical Review A}, author={Duan, Bojia and Yuan, Jiabin and Liu, Ying and Li, Dan}, year={2018}}
@article{lin_bao_zhang_li_wang_2019, title={An improved quantum principal component analysis algorithm based on the quantum singular threshold method}, volume={383}, DOI={10.1016/j.physleta.2019.06.026}, number={24}, journal={Physics Letters A}, author={Lin, Jie and Bao, Wan-Su and Zhang, Shuo and Li, Tan and Wang, Xiang}, year={2019}, pages={2862–2868}}
@article{fang_guo_ding_lan_2014, title={An Improved Singular Value Decomposition Recommender Algorithm Based on Local Structures}, volume={35}, DOI={10.3724/sp.j.1146.2012.01299}, number={6}, journal={Journal of Electronics \& Information Technology}, author={Fang, Yao-Ning and Guo, Yun-Fei and Ding, Xue-Tao and Lan, Ju-Long}, year={2014}, pages={1284–1289}}
@article{alter_brown_botstein_2000, title={Singular value decomposition for genome-wide expression data processing and modeling}, volume={97}, DOI={10.1073/pnas.97.18.10101}, number={18}, journal={Proceedings of the National Academy of Sciences}, author={Alter, O. and Brown, P. O. and Botstein, D.}, year={2000}, pages={10101–10106}}
@INPROCEEDINGS{image_compression_svd,
author={Prasantha, H.S. and Shashidhara, H.L. and Balasubramanya Murthy, K.N.},
booktitle={International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2007)},
title={Image Compression Using SVD},
year={2007},
volume={3},
number={},
pages={143-145},
doi={10.1109/ICCIMA.2007.386}}
@article{baeza-yates_boldi_castillo_2006, title={Generalizing PageRank}, DOI={10.1145/1148170.1148225}, journal={Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR 06}, author={Baeza-Yates, Ricardo and Boldi, Paolo and Castillo, Carlos}, year={2006}}
@techreport{haveliwala_2003,
number = {2003-35},
month = {June},
author = {Taher Haveliwala and Sepandar Kamvar and Glen Jeh},
title = {An Analytical Comparison of Approaches to Personalizing PageRank},
type = {Technical Report},
publisher = {Stanford},
institution = {Stanford InfoLab},
year = {2003},
url = {http://ilpubs.stanford.edu:8090/596/},
abstract = {PageRank, the popular link-analysis algorithm for ranking web pages, assigns a query and user independent estimate of "importance" to web pages. Query and user sensitive extensions of PageRank, which use a basis set of biased PageRank vectors, have been proposed in order to personalize the ranking function in a tractable way. We analytically compare three recent approaches to personalizing PageRank and discuss the tradeoffs of each one.}
}
@article{boldi_2005, title={TotalRank}, DOI={10.1145/1062745.1062787}, journal={Special interest tracks and posters of the 14th international conference on World Wide Web - WWW 05}, author={Boldi, Paolo}, year={2005}}
@article{yang_king_lyu_2007, title={DiffusionRank}, DOI={10.1145/1277741.1277815}, journal={Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval - SIGIR 07}, author={Yang, Haixuan and King, Irwin and Lyu, Michael R.}, year={2007}}
@article{boldi_posenato_santini_vigna, title={Traps and Pitfalls of Topic-Biased PageRank}, DOI={10.1007/978-3-540-78808-9_10}, journal={Algorithms and Models for the Web-Graph Lecture Notes in Computer Science}, author={Boldi, Paolo and Posenato, Roberto and Santini, Massimo and Vigna, Sebastiano}, pages={107–116}}
@article{montenegro_tetali_2005, title={Mathematical Aspects of Mixing Times in Markov Chains}, DOI={10.1561/9781933019772}, author={Montenegro, R and Tetali, P}, year={2005}}
@article{coulhon_grigoryan_1998, title={Random Walks on Graphs with Regular Volume Growth}, volume={8}, DOI={10.1007/s000390050070}, number={4}, journal={Geometric And Functional Analysis}, author={Coulhon, T. and Grigoryan, A.}, year={1998}, pages={656–701}}
@article{sardellitti_barbarossa_lorenzo_2017, title={Graph Fourier Transform for directed graphs based on Lovász extension of min-cut}, DOI={10.1109/icassp.2017.7952886}, journal={2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, author={Sardellitti, Stefania and Barbarossa, Sergio and Lorenzo, Paolo Di}, year={2017}}
@book{hoffman_kunze_1962, place={Englewood Cliffs, NJ, Prentice-Hall}, title={Linear Algebra, by Kenneth Hoffman and Ray Kunze}, author={Hoffman, Kenneth and Kunze, Ray Alden}, year={1962}}
@article{sandryhaila_moura_2014, title={Discrete Signal Processing on Graphs: Frequency Analysis}, volume={62}, DOI={10.1109/tsp.2014.2321121}, number={12}, journal={IEEE Transactions on Signal Processing}, author={Sandryhaila, Aliaksei and Moura, Jose M. F.}, year={2014}, pages={3042–3054}}
@article{shuman_narang_frossard_ortega_vandergheynst_2013, title={The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains}, volume=30, DOI={10.1109/msp.2012.2235192}, number=3, journal={IEEE Signal Processing Magazine}, author={Shuman, D. I. and Narang, S. K. and Frossard, P. and Ortega, A. and Vandergheynst, P.}, year=2013, pages={83–98}}
@article{ricaud_borgnat_tremblay_goncalves_vandergheynst_2019, title={Fourier could be a data scientist: From graph Fourier transform to signal processing on graphs}, volume={20}, DOI={10.1016/j.crhy.2019.08.003}, number={5}, journal={Comptes Rendus Physique}, author={Ricaud, Benjamin and Borgnat, Pierre and Tremblay, Nicolas and Gonçalves, Paulo and Vandergheynst, Pierre}, year={2019}, pages={474–488}}
@article{sarma_molla_pandurangan_upfal_2013, title={Fast Distributed PageRank Computation}, DOI={10.1007/978-3-642-35668-1_2}, journal={Distributed Computing and Networking Lecture Notes in Computer Science}, author={Sarma, Atish Das and Molla, Anisur Rahaman and Pandurangan, Gopal and Upfal, Eli}, year={2013}, pages={11–26}}
@book{levin_peres_wilmer_propp_wilson_2017, place={Providence, RI}, title={Markov chains and mixing times}, publisher={American Mathematical Society}, author={Levin, David Asher and Peres, Y. and Wilmer, Elizabeth L. and Propp, James and Wilson, David B.}, year={2017}}
@article{aharonov_dam_kempe_landau_lloyd_regev_2008, title={Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation}, volume={50}, DOI={10.1137/080734479}, number={4}, journal={SIAM Review}, author={Aharonov, Dorit and Dam, Wim Van and Kempe, Julia and Landau, Zeph and Lloyd, Seth and Regev, Oded}, year={2008}, pages={755–787}}
@article{speedup_via_quantum_sampling,
title = {Speedup via quantum sampling},
author = {Wocjan, Pawel and Abeyesinghe, Anura},
journal = {Phys. Rev. A},
volume = {78},
issue = {4},
pages = {042336},
numpages = {8},
year = {2008},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.78.042336},
url = {https://link.aps.org/doi/10.1103/PhysRevA.78.042336}
}
@article{manzano_2020, title={A short introduction to the Lindblad master equation}, volume={10}, DOI={10.1063/1.5115323}, number={2}, journal={AIP Advances}, author={Manzano, Daniel}, year={2020}, pages={025106}}
@article{kempe_2009, title={Quantum random walks: an introductory overview}, volume={50}, DOI={10.1080/00107510902734722}, number={1}, journal={Contemporary Physics}, author={Kempe, J.}, year={2009}, pages={339–359}}
@article{kerenidis2016,
title={Quantum Recommendation Systems},
author={Iordanis Kerenidis and Anupam Prakash},
journal={ArXiv},
year={2017},
volume={abs/1603.08675}
}
@article{lawler_limic, title={Introduction}, DOI={10.1017/cbo9780511750854.002}, journal={Random Walk: A Modern Introduction}, author={Lawler, Gregory F. and Limic, Vlada}, pages={1–20}}
@misc{wikipedia_2021_random_walk, title={Random walk}, url={https://en.wikipedia.org/wiki/Random_walk}, journal={Wikipedia}, publisher={Wikimedia Foundation}, year={2021}, month={Jul}}
@article{kleinberg_1999, title={Authoritative sources in a hyperlinked environment}, volume={46}, DOI={10.1145/324133.324140}, number={5}, journal={Journal of the ACM}, author={Kleinberg, Jon M.}, year={1999}, pages={604–632}}
@article{barabasi_albert_1999, title={Emergence of Scaling in Random Networks}, volume={286}, DOI={10.1126/science.286.5439.509}, number={5439}, journal={Science}, author={Barabási, Albert-László and Albert, Réka}, year={1999}, pages={509–512}}
@article{albert_barabasi_2002, title={Statistical mechanics of complex networks}, volume={74}, DOI={10.1103/revmodphys.74.47}, number={1}, journal={Reviews of Modern Physics}, author={Albert, Réka and Barabási, Albert-László}, year={2002}, pages={47–97}}
@article{choromanski_matuszak_mie, title={Scale-Free Graph with Preferential Attachment and Evolving Internal Vertex Structure}, volume={151}, DOI={10.1007/s10955-013-0749-1}, number={6}, journal={Journal of Statistical Physics}, author={Choromański, Krzysztof and Matuszak, Michal and Miekisz Jacek}, year={2013}, pages={1175–1183}}
@article{erdos, title={On Random Graphs. I}, volume={6}, journal={Publicationes Mathematicae}, author={Erdős, P.; Rényi, A.}, year={1959}, pages={290-297}}
@article{kleinberg_hubs,
author = {Kleinberg, Jon M.},
title = {Hubs, Authorities, and Communities},
year = {1999},
issue_date = {Dec. 1999},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {31},
number = {4es},
issn = {0360-0300},
url = {https://doi.org/10.1145/345966.345982},
doi = {10.1145/345966.345982},
journal = {ACM Comput. Surv.},
month = dec,
pages = {5–es},
numpages = {3},
keywords = {link analysis, hypertext structure, World Wide Web, graph algorithms}
}
@article{whitfield_rodriguez-rosario_aspuru-guzik_2010, title={Quantum stochastic walks: A generalization of classical random walks and quantum walks}, volume={81}, DOI={10.1103/physreva.81.022323}, number={2}, journal={Physical Review A}, author={Whitfield, James D. and Rodríguez-Rosario, César A. and Aspuru-Guzik, Alán}, year={2010}}
@book{grinstead_snell_2006, place={Providence}, title={Introduction to probability}, publisher={American Mathematical Society}, author={Grinstead, Charles Miller and Snell, J. Laurie}, year={2006}}
@article{meyer_2000, title={Matrix Analysis and Applied Linear Algebra}, DOI={10.1137/1.9780898719512}, author={Meyer, Carl}, year={2000}}
@article{szegedy, title={Quantum Speed-Up of Markov Chain Based Algorithms}, DOI={10.1109/focs.2004.53}, journal={45th Annual IEEE Symposium on Foundations of Computer Science}, author={Szegedy, M.}}
@article{loke_tang_rodriguez_small_wang_2016, title={Comparing classical and quantum PageRanks}, volume={16}, DOI={10.1007/s11128-016-1456-z}, number={1}, journal={Quantum Information Processing}, author={Loke, T. and Tang, J. W. and Rodriguez, J. and Small, M. and Wang, J. B.}, year={2016}}
@article{sanchez-burillo_duch_gomez-gardenes_zueco_2012, title={Quantum Navigation and Ranking in Complex Networks}, volume={2}, DOI={10.1038/srep00605}, number={1}, journal={Scientific Reports}, author={Sánchez-Burillo, Eduardo and Duch, Jordi and Gómez-Gardeñes, Jesús and Zueco, David}, year={2012}}
@article{gleich_2015, title={PageRank Beyond the Web}, volume={57}, DOI={10.1137/140976649}, number={3}, journal={SIAM Review}, author={Gleich, David F.}, year={2015}, pages={321–363}}
@misc{cornell_pagerank, title={Networks}, url={https://blogs.cornell.edu/info2040/2014/11/03/more-than-just-a-web-search-algorithm-googles-pagerank-in-non-internet-contexts/}, journal={More than just a Web Search algorithm: Google's PageRank in non-Internet contexts : Networks Course blog for INFO 2040/CS 2850/Econ 2040/SOC 2090}}
@article{rebentrost_steffens_marvian_lloyd_2018, title={Quantum singular-value decomposition of nonsparse low-rank matrices}, volume={97}, DOI={10.1103/physreva.97.012327}, number={1}, journal={Physical Review A}, author={Rebentrost, Patrick and Steffens, Adrian and Marvian, Iman and Lloyd, Seth}, year={2018}}
@article{gilyen_su_low_wiebe_2019, title={Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics}, DOI={10.1145/3313276.3316366}, journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing}, author={Gilyén, András and Su, Yuan and Low, Guang Hao and Wiebe, Nathan}, year={2019}}
@article{tepper2016, title={A short-graph fourier transform via personalized pagerank vectors}, DOI={10.1109/icassp.2016.7472590}, journal={2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, author={Tepper, Mariano and Sapiro, Guillermo}, year={2016}}
@article{google2019,
title = {Quantum Supremacy using a Programmable Superconducting Processor},
author = {Frank Arute and Kunal Arya and Ryan Babbush and Dave Bacon and Joseph Bardin and Rami Barends, et al},
year = {2019},
URL = {https://www.nature.com/articles/s41586-019-1666-5},
journal = {Nature},
pages = {505–510},
volume = {574}
}
@misc{sevi2019,
title={Harmonic analysis on directed graphs and applications: from Fourier analysis to wavelets},
author={Harry Sevi and Gabriel Rilling and Pierre Borgnat},
year={2019},
eprint={1811.11636},
archivePrefix={arXiv},
primaryClass={math.FA}
}
@article{bacon2010,
author = {Dave Bacon},
title = {The Quantum Fourier Transform and Jordan’s Algorithm},
annote = {Exhaustive presentation of Quantum Fourier Transform.}
}
@article{Rebenstrot2014,
author = {Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd},
title = {Quantum support vector machine for big data classification},
year = {2014},
month = {Juillet},
journal = {ArXiv},
annote = {Utilisation du calcul quantique dans le calcul de SVM (big data) en avec une complexité logarithmique}
}
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