I References

Aaronson, Scott, and Patrick Rall. 2020. “Quantum Approximate Counting, Simplified.” In Symposium on Simplicity in Algorithms, 24–32. SIAM.
Ahmadi, Hamed, and Chen-Fu Chiang. 2010. “Quantum Phase Estimation with Arbitrary Constant-Precision Phase Shift Operators.” arXiv Preprint arXiv:1012.4727.
Ambainis, A. 2012. “Variable Time Amplitude Amplification and a Faster Quantum Algorithm for Solving Systems of Linear Equations 29th Int.” In Symp. Theoretical Aspects of Computer Science (STACS 2012), 14:636–47.
Ambainis, Andris. 2002. “Quantum Lower Bounds by Quantum Arguments.” Journal of Computer and System Sciences 64 (4): 750–67.
———. 2012. “Variable Time Amplitude Amplification and Quantum Algorithms for Linear Algebra Problems.” In STACS’12 (29th Symposium on Theoretical Aspects of Computer Science), 14:636–47. LIPIcs.
Ambainis, Andris, Kaspars Balodis, Jānis Iraids, Martins Kokainis, Krišjānis Prūsis, and Jevgēnijs Vihrovs. 2019. “Quantum Speedups for Exponential-Time Dynamic Programming Algorithms.” In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 1783–93. SIAM.
Andrew, Childs. 2017. “Lecture Notes on Quantum Algorithms.” https://www.cs.umd.edu/~amchilds/qa/.
Arthur, David, and Sergei Vassilvitskii. 2006. “How Slow Is the k-Means Method?” In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, 144–53. ACM.
———. 2007. “K-Means++: The Advantages of Careful Seeding.” In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1027–35. Society for Industrial; Applied Mathematics.
Bellante, Armando. 2020. “Quantum Singular Value Estimation Techniques for Data Representation.” Https://Www. Politesi. Polimi. It/Handle/10589/166445.
Berkes, P., and L. Wiskott. 2005. Slow feature analysis yields a rich repertoire of complex cell properties.” Journal of Vision 5 (6).
Berkes, Pietro. 2005. Pattern Recognition with Slow Feature Analysis.” Cognitive Sciences EPrint Archive (CogPrints) 4104.
Berry, Dominic W, Andrew M Childs, Richard Cleve, Robin Kothari, and Rolando D Somma. 2015. “Simulating Hamiltonian Dynamics with a Truncated Taylor Series.” Physical Review Letters 114 (9): 090502.
Berry, Dominic W, Andrew M Childs, and Robin Kothari. 2015. “Hamiltonian Simulation with Nearly Optimal Dependence on All Parameters.” In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 792–809. IEEE.
Biernacki, Christophe, Gilles Celeux, and Gérard Govaert. 2003. “Choosing Starting Values for the EM Algorithm for Getting the Highest Likelihood in Multivariate Gaussian Mixture Models.” Computational Statistics & Data Analysis 41 (3-4): 561–75.
Blaschke, Tobias, and Laurenz Wiskott. 2004. “Independent Slow Feature Analysis and Nonlinear Blind Source Separation.” In International Conference on Independent Component Analysis and Signal Separation, 742–49. Springer.
Blömer, Johannes, and Kathrin Bujna. 2013. “Simple Methods for Initializing the EM Algorithm for Gaussian Mixture Models.” CoRR.
Borga, Magnus, Tomas Landelius, and Hans Knutsson. 1997. A Unified Approach to Pca, Pls, Mlr and Cca. Linköping University, Department of Electrical Engineering.
Boyer, Michel, Gilles Brassard, Peter Høyer, and Alain Tapp. 1998. “Tight Bounds on Quantum Searching.” Fortschritte Der Physik: Progress of Physics 46 (4-5): 493–505.
Brassard, Gilles, Frederic Dupuis, Sebastien Gambs, and Alain Tapp. 2011. “An Optimal Quantum Algorithm to Approximate the Mean and Its Application for Approximating the Median of a Set of Points over an Arbitrary Distance.” arXiv Preprint arXiv:1106.4267.
Brassard, Gilles, Peter Hoyer, Michele Mosca, and Alain Tapp. 2002. “Quantum Amplitude Amplification and Estimation.” Contemporary Mathematics 305: 53–74.
Buhrman, Harry, Richard Cleve, Ronald De Wolf, and Christof Zalka. 1999. “Bounds for Small-Error and Zero-Error Quantum Algorithms.” In 40th Annual Symposium on Foundations of Computer Science (Cat. No. 99cb37039), 358–68. IEEE.
Celeux, Gilles, and Gérard Govaert. 1992. “A Classification EM Algorithm for Clustering and Two Stochastic Versions.” Computational Statistics & Data Analysis 14 (3): 315–32.
Chakraborty, Shantanav, András Gilyén, and Stacey Jeffery. 2019. “The Power of Block-Encoded Matrix Powers: Improved Regression Techniques via Faster Hamiltonian Simulation.” In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
Childs, Andrew M, Robin Kothari, and Rolando D Somma. 2015. Quantum linear systems algorithm with exponentially improved dependence on precision.”
Childs, Andrew M, and Nathan Wiebe. 2012. “Hamiltonian Simulation Using Linear Combinations of Unitary Operations.” arXiv Preprint arXiv:1202.5822.
Church, Kenneth W, and William A Gale. 1995. “Poisson Mixtures.” Natural Language Engineering 1 (2): 163–90.
Cong, Iris, and Luming Duan. 2015. “Quantum Discriminant Analysis for Dimensionality Reduction and Classification.” arXiv Preprint arXiv:1510.00113.
De Bie, Tijl, Nello Cristianini, and Roman Rosipal. 2005. “Eigenproblems in Pattern Recognition.” In Handbook of Geometric Computing, 129–67. Springer.
De Wolf, Ronald. 2019. “Quantum Computing: Lecture Notes.” arXiv:1907.09415.
Deerwester, Scott, Susan T Dumais, George W Furnas, Thomas K Landauer, and Richard Harshman. 1990. “Indexing by Latent Semantic Analysis.” Journal of the American Society for Information Science 41 (6): 391–407. https://doi.org/10.1002/(SICI)1097-4571(199009)41:6<391::AID-ASI1>3.0.CO;2-9.
Dexter, AR, and DW Tanner. 1972. “Packing Densities of Mixtures of Spheres with Log-Normal Size Distributions.” Nature Physical Science 238 (80): 31.
Dörn, Sebastian. 2008. “Quantum Complexity of Graph and Algebraic Problems.” PhD thesis, Universität Ulm.
Drineas, Petros, Iordanis Kerenidis, and Prabhakar Raghavan. 2002. “Competitive Recommendation Systems.” In Proceedings of the Thiry-Fourth Annual ACM Symposium on Theory of Computing, 82–90. ACM.
Duan, Bojia, Jiabin Yuan, Chao-Hua Yu, Jianbang Huang, and Chang-Yu Hsieh. 2020. “A Survey on HHL Algorithm: From Theory to Application in Quantum Machine Learning.” Physics Letters A 384 (24): 126595.
Durr, Christoph, and Peter Hoyer. 1996. “A Quantum Algorithm for Finding the Minimum.” arXiv Preprint Quant-Ph/9607014.
Dürr, Christoph, Mark Heiligman, Peter HOyer, and Mehdi Mhalla. 2006. “Quantum Query Complexity of Some Graph Problems.” SIAM Journal on Computing 35 (6): 1310–28.
Dürr, Christoph, Mark Heiligman, Peter Høyer, and Mehdi Mhalla. 2004. Quantum query complexity of some graph problems *.” http://arxiv.org/abs/0401091v2.
Escalante-B, Alberto N, and Laurenz Wiskott. 2012. “Slow Feature Analysis: Perspectives for Technical Applications of a Versatile Learning Algorithm.” KI-Künstliche Intelligenz 26 (4): 341–48.
Ghitany, ME, Ross A Maller, and S Zhou. 1994. “Exponential Mixture Models with Long-Term Survivors and Covariates.” Journal of Multivariate Analysis 49 (2): 218–41.
Ghojogh, Benyamin, Fakhri Karray, and Mark Crowley. 2019. “Eigenvalue and Generalized Eigenvalue Problems: Tutorial.” arXiv Preprint arXiv:1903.11240.
Gilyén, András, and Tongyang Li. 2019. “Distributional Property Testing in a Quantum World.” arXiv Preprint arXiv:1902.00814.
Gilyén, András, Yuan Su, Guang Hao Low, and Nathan Wiebe. 2019. “Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics.” In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 193–204.
Giovannetti, Vittorio, Seth Lloyd, and Lorenzo Maccone. 2008. Quantum random access memory.” Physical Review Letters 100 (16): 160501.
Greenacre, Michael J. 1984. “Theory and Applications of Correspondence Analysis.”
Gribling, Sander. 2019. “Applications of Optimization to Factorization Ranks and Quantum Information Theory.”
Grinko, Dmitry, Julien Gacon, Christa Zoufal, and Stefan Woerner. 2019. “Iterative Quantum Amplitude Estimation.” arXiv Preprint arXiv:1912.05559.
Grover, Lov K. 2005. “Fixed-Point Quantum Search.” Physical Review Letters 95 (15): 150501.
Gu, Xingjian, Chuancai Liu, and Sheng Wang. 2013. Supervised Slow Feature Analysis for Face Recognition.” In, 178–84. http://link.springer.com/10.1007/978-3-319-02961-0\%5F22.
Hamoudi, Yassine, and Frédéric Magniez. 2018. “Quantum Chebyshev’s Inequality and Applications.” arXiv Preprint arXiv:1807.06456.
Hamoudi, Yassine, Maharshi Ray, Patrick Rebentrost, Miklos Santha, Xin Wang, and Siyi Yang. 2020. “Quantum Algorithms for Hedging and the Sparsitron.” arXiv Preprint arXiv:2002.06003.
Harrow, Aram W., Avinatan Hassidim, and Seth Lloyd. 2009. Quantum Algorithm for Linear Systems of Equations.” Physical Review Letters 103 (15): 150502. http://link.aps.org/doi/10.1103/PhysRevLett.103.150502.
Harun-Ur-Rashid. 2018. “Research Paper Dataset.” Https://Www. Kaggle. Com/Harunshimanto/Research-Paper.
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2009. The Elements of Statistical Learning. Vol. 1. Springer Series in Statistics. New York, NY: Springer New York. http://www.springerlink.com/index/10.1007/b94608.
Heinrich, Stefan. 2002. “Quantum Summation with an Application to Integration.” Journal of Complexity 18 (1): 1–50.
Hogan, Robin. 2006. “How to Combine Errors.”
Hsu, Hsiang, Salman Salamatian, and Flavio P Calmon. 2019. “Correspondence Analysis Using Neural Networks.” In The 22nd International Conference on Artificial Intelligence and Statistics, 2671–80.
Huang, Hsin-Yuan, Kishor Bharti, and Patrick Rebentrost. 2019. “Near-Term Quantum Algorithms for Linear Systems of Equations.” arXiv Preprint arXiv:1909.07344.
Jerrum, Mark R, Leslie G Valiant, and Vijay V Vazirani. 1986. “Random Generation of Combinatorial Structures from a Uniform Distribution.” Theoretical Computer Science 43: 169–88.
Kalai, Adam Tauman, Ankur Moitra, and Gregory Valiant. 2012. “Disentangling Gaussians.” Communications of the ACM 55 (2): 113–20.
Kapoor, Ashish, Nathan Wiebe, and Krysta Svore. 2016. “Quantum Perceptron Models.” In Advances in Neural Information Processing Systems, 3999–4007.
Kennedy, Tom. 2016. Chapter2: Basics of direct Monte Carlo.” https://www.math.arizona.edu/~tgk/mc/book_chap2.pdf.
Kerenidis, Iordanis, Jonas Landman, Alessandro Luongo, and Anupam Prakash. 2019. “Q-Means: A Quantum Algorithm for Unsupervised Machine Learning.” In Advances in Neural Information Processing Systems, 4136–46.
Kerenidis, Iordanis, Jonas Landman, and Anupam Prakash. 2019. “Quantum Algorithms for Deep Convolutional Neural Networks.” arXiv Preprint arXiv:1911.01117.
Kerenidis, Iordanis, and Alessandro Luongo. 2020. “Classification of the MNIST Data Set with Quantum Slow Feature Analysis.” Physical Review A 101 (6): 062327.
Kerenidis, Iordanis, and Anupam Prakash. 2017a. “Quantum Gradient Descent for Linear Systems and Least Squares.” arXiv:1704.04992.
———. 2017b. “Quantum Recommendation Systems.” Proceedings of the 8th Innovations in Theoretical Computer Science Conference.
———. 2018. “A Quantum Interior Point Method for LPs and SDPs.” arXiv:1808.09266.
———. 2020. “Quantum Gradient Descent for Linear Systems and Least Squares.” Physical Review A 101 (2): 022316.
Kitaev, A Yu. 1996. “Quantum Measurements and the Abelian Stabilizer Problem.” In Electronic Colloq. On Computational Complexity.
Krizhevsky, Alex, and others. 2009. “Learning Multiple Layers of Features from Tiny Images.”
Ku, Harry H, and others. 1966. “Notes on the Use of Propagation of Error Formulas.” Journal of Research of the National Bureau of Standards 70 (4): 263–73.
LeCun, Yann. 1998. “The MNIST Database of Handwritten Digits.” Http://Yann. Lecun. Com/Exdb/Mnist/.
Liu, Chuanhai, and Donald B Rubin. 1995. ML Estimation of the t Distribution Using EM and Its Extensions, ECM and ECME.” Statistica Sinica, 19–39.
Lloyd, Seth, Masoud Mohseni, and Patrick Rebentrost. 2014. “Quantum Principal Component Analysis.” Nature Physics 10 (9): 631.
Lloyd, Stuart. 1982. “Least Squares Quantization in PCM.” IEEE Transactions on Information Theory 28 (2): 129–37.
Low, Guang Hao, and Isaac L Chuang. 2017. “Hamiltonian Simulation by Uniform Spectral Amplification.” arXiv Preprint arXiv:1707.05391.
———. 2019. “Hamiltonian Simulation by Qubitization.” Quantum 3: 163.
Manara, M. P., A. Perotti, and R. Scapellato. 2007. Geometria e Algebra Lineare. Esculapio.
Markov. 1890. “On a Question by d. I. Mendeleev.” Zap. Imp. Akad. Nauk. St. Petersburg.
Mitchell, Tom M, and others. 1997. “Machine Learning.”
Miyahara, Hideyuki, Kazuyuki Aihara, and Wolfgang Lechner. 2020. “Quantum Expectation-Maximization Algorithm.” Physical Review A 101 (1): 012326.
Moitra, Ankur. 2018. Algorithmic Aspects of Machine Learning. Cambridge University Press.
Montanaro, Ashley. 2015. “Quantum Speedup of Monte Carlo Methods.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2181): 20150301.
Murphy, Kevin P. 2012. Machine Learning: A Probabilistic Perspective. MIT press.
Nannicini, Giacomo. 2019. “Fast Quantum Subroutines for the Simplex Method.” arXiv Preprint arXiv:1910.10649.
Ng, Andrew. 2012. “Cs229 Lecture Notes - Machine Learning.”
Nielsen, Michael A, and Isaac Chuang. 2002. “Quantum Computation and Quantum Information.” AAPT.
O’Donnell, Ryan. 2015. “Lecture 13: Lower Bounds Using the Adversary Method.” Carnegie Mellon University.
O’Donnell, Ryan, and John Wright. 2016. “Efficient Quantum Tomography.” In Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing, 899–912.
Otterbach, JS, R Manenti, N Alidoust, A Bestwick, M Block, B Bloom, S Caldwell, et al. 2017. “Unsupervised Machine Learning on a Hybrid Quantum Computer.” arXiv Preprint arXiv:1712.05771.
Paturi, Ramamohan. 1992. “On the Degree of Polynomials That Approximate Symmetric Boolean Functions (Preliminary Version).” In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, 468–74. STOC ’92. New York, NY, USA: Association for Computing Machinery. https://doi.org/10.1145/129712.129758.
Pedregosa, F., G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, et al. 2011. “Scikit-Learn: Machine Learning in Python.” Journal of Machine Learning Research 12: 2825–30.
Prakash, Anupam. 2014. “Quantum Algorithms for Linear Algebra and Machine Learning.” PhD thesis, EECS Department, University of California, Berkeley. http://www2.eecs.berkeley.edu/Pubs/TechRpts/2014/EECS-2014-211.html.
Rebentrost, Patrick, and Seth Lloyd. 2018. “Quantum Computational Finance: Quantum Algorithm for Portfolio Optimization.” arXiv Preprint arXiv:1811.03975 98 (4): 042308.
Rudin, Walter, and others. 1964. Principles of Mathematical Analysis. Vol. 3. McGraw-hill New York.
Schlesinger, Enrico. 2011. Algebra Lineare e Geometria. Zanichelli.
Schuld, Maria, and Francesco Petruccione. 2018. Supervised Learning with Quantum Computers. Vol. 17. Springer.
Schuld, Maria, Ilya Sinayskiy, and Francesco Petruccione. 2015. An introduction to quantum machine learning.” Contemporary Physics 56 (2): 172–85. https://doi.org/10.1080/00107514.2014.964942.
Sprekeler, Henning, and Laurenz Wiskott. 2008. Understanding Slow Feature Analysis: A Mathematical Framework.” Cognitive Sciences EPrint Archive (CogPrints) 6223.
Strang, Gilbert. 2016. Introduction to Linear Algebra. Wellesley - Cambridge Press.
Subramanian, Sathyawageeswar, Stephen Brierley, and Richard Jozsa. 2019. “Implementing Smooth Functions of a Hermitian Matrix on a Quantum Computer.” Journal of Physics Communications 3 (6): 065002.
Sun, Lin, Kui Jia, Tsung-Han Chan, Yuqiang Fang, Gang Wang, and Shuicheng Yan. 2014. “DL-SFA: Deeply-Learned Slow Feature Analysis for Action Recognition.” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2625–32.
Ta-Shma, Amnon. 2013. “Inverting Well Conditioned Matrices in Quantum Logspace.” In Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, 881–90.
Van Apeldoorn, Joran, András Gilyén, Sander Gribling, and Ronald de Wolf. 2020. “Quantum SDP-Solvers: Better Upper and Lower Bounds.” Quantum 4: 230.
Walter, Michael. 2018. “Symmetry and Quantum Information.”
Wiebe, Nathan, Ashish Kapoor, and Krysta M Svore. 2018. “Quantum Nearest-Neighbor Algorithms for Machine Learning.” Quantum Information and Computation 15.
Wiskott, L., P. Berkes, M. Franzius, H. Sprekeler, and N. Wilbert. 2011. Slow Feature Analysis.” Scholarpedia 6 (4): 5282.
Wiskott Laurenz, and Laurenz Wiskott. 1999. Learning invariance manifolds.” Neurocomputing 26-27: 925–32. https://doi.org/10.1016/S0925-2312(99)00011-9.
Wocjan, Pawel, Chen-Fu Chiang, Daniel Nagaj, and Anura Abeyesinghe. 2009. “Quantum Algorithm for Approximating Partition Functions.” Physical Review A 80 (2): 022340.
Xiao, Han, Kashif Rasul, and Roland Vollgraf. 2017. “Fashion-MNIST: A Novel Image Dataset for Benchmarking Machine Learning Algorithms.” arXiv Preprint Cs.LG/1708.07747, August.
Yin, Jianhua, and Jianyong Wang. 2014. “A Dirichlet Multinomial Mixture Model-Based Approach for Short Text Clustering.” In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 233–42. ACM.
Yoder, Theodore J, Guang Hao Low, and Isaac L Chuang. 2014. “Fixed-Point Quantum Search with an Optimal Number of Queries.” Physical Review Letters 113 (21): 210501.
Yu, Chao-Hua, Fei Gao, Song Lin, and Jingbo Wang. 2019. “Quantum Data Compression by Principal Component Analysis.” Quantum Information Processing 18 (8): 249. https://doi.org/10.1007/s11128-019-2364-9.
Zhang, Kaining, Min-Hsiu Hsieh, Liu Liu, and Dacheng Tao. 2020. “Efficient State Read-Out for Quantum Machine Learning Algorithms.” arXiv Preprint arXiv:2004.06421.
Zhang Zhang, and Dacheng Tao. 2012. Slow Feature Analysis for Human Action Recognition.” IEEE Transactions on Pattern Analysis and Machine Intelligence 34 (3): 436–50. http://ieeexplore.ieee.org/document/6136516/.
Zhao, Liming, Carlos A Pérez-Delgado, and Joseph F Fitzsimons. 2016. “Fast Graph Operations in Quantum Computation.” Physical Review A 93 (3): 032314.