Bibliografía

Bibliografía#

1

Reglas de born. URL: https://publish.obsidian.md/myquantumwell/Quantum+Mechanics/Quantum+Measurement/Born+rule.

2

Catalina Albornoz. How to start learning quantum machine learning. URL: https://pennylane.ai/blog/2021/10/how-to-start-learning-quantum-machine-learning/.

3

aprendemachinelearning. Comprende principal. URL: https://www.aprendemachinelearning.com/comprende-principal-component-analysis/.

4

V. Robles B. Descenso por gradiente: una breve introducción - parte 1. URL: vlarobbyk/descenso-por-gradiente.

5

Nils Barth. The gramian and k-volume in n-space: some classical results in linear algebra. Journal of Young Investigators, 1999.

6

Universitat Oberta Catalunya. Concavidad y convexidad de una función. URL: http://cimanet.uoc.edu/cursMates0/IniciacionMatematicas/s11/2_6_8.html.

7

M.¬†Cerezo, Andrew Arrasmith, Ryan Babbush, Simon¬†C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod¬†R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick¬†J. Coles. Variational quantum algorithms. Nature Reviews Physics, 3(9):625‚Äď644, August 2021. URL: http://dx.doi.org/10.1038/s42254-021-00348-9, doi:10.1038/s42254-021-00348-9.

8

C.¬†Cortes and V.¬†Vapnik. Support vector networks. Machine Learning, 20:273‚Äď297, 1995. doi:https://doi.org/10.1007/BF00994018.

9

Coursera. Gradient descent with momentum. URL: https://www.coursera.org/lecture/deep-neural-network/gradient-descent-with-momentum-y0m1f.

10

Juankboards en Planeta Chatbot. Conceptos fundamentales en machine learning: función de pérdida y optimización. URL: https://planetachatbot.com/conceptos-fundamentales-en-machine-learning-funcon-de-perdida-y-optimizacion/.

11

R.¬†A. Fisher. The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(7):179‚Äď188, 1936.

12

Institute for Quantum Computing. Quantum kernel methods. URL: PaddlePaddle/Quantum.

13

geeksforgeeks. The ultimate guide to quantum machine learning ‚Äď the next big thing. URL: https://www.geeksforgeeks.org/the-ultimate-guide-to-quantum-machine-learning-the-next-big-thing/.

14

Marc¬†G Genton. Classes of kernels for machine learning: a statistics perspective. Journal of machine learning research, 2(Dec):299‚Äď312, 2001.

15

Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The elements of statistical learning: data mining, inference and prediction. Springer, 2 edition, 2009. URL: http://www-stat.stanford.edu/~tibs/ElemStatLearn/.

16

Vojtńõch Havl√≠ńćek, Antonio¬†D. C√≥rcoles, Kristan Temme, Aram¬†W. Harrow, Abhinav Kandala, Jerry¬†M. Chow, and Jay¬†M. Gambetta. Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747):209‚Äď212, March 2019. URL: http://dx.doi.org/10.1038/s41586-019-0980-2, doi:10.1038/s41586-019-0980-2.

17

Thomas Hofmann, Bernhard Sch√∂lkopf, and Alexander¬†J. Smola. Kernel methods in machine learning. The Annals of Statistics, 36(3):1171 ‚Äď 1220, 2008. URL: https://doi.org/10.1214/009053607000000677, doi:10.1214/009053607000000677.

18

Hsin-Yuan Huang, Mick Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R. McClean. Power of data in quantum machine learning. Nature Communications, 2020. URL: https://api.semanticscholar.org/CorpusID:226246283.

19

IBM. Quantum machine learning course. URL: https://learn.qiskit.org/course/machine-learning/introduction.

20

IBM. ¬Ņqu√© es el descenso de gradiente? URL: https://www.ibm.com/mx-es/topics/gradient-descent.

21

IBM. ¬Ņqu√© es machine learning? URL: https://www.ibm.com/es-es/topics/machine-learning.

22

Keras. Adadelta. URL: https://keras.io/api/optimizers/adadelta/.

23

Diederik P Kingma and Jimmy Ba. Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.

24

Seth Lloyd, Maria Schuld, Aroosa Ijaz, Josh Izaac, and Nathan Killoran. Quantum embeddings for machine learning. 2020. arXiv:2001.03622.

25

Antonio Macaluso, Luca Clissa, Stefano Lodi, and Claudio Sartori. A variational algorithm for quantum neural networks. In Valeria¬†V. Krzhizhanovskaya, G√°bor Z√°vodszky, Michael¬†H. Lees, Jack¬†J. Dongarra, Peter M.¬†A. Sloot, S√©rgio Brissos, and Jo√£o Teixeira, editors, Computational Science ‚Äď ICCS 2020, 591‚Äď604. Cham, 2020. Springer International Publishing.

26

Jose Martinez. Gradiente descendiente. URL: https://www.iartificial.net/gradiente-descendiente-para-aprendizaje-automatico/.

27

Mikko Mottonen, Juha J. Vartiainen, Ville Bergholm, and Martti M. Salomaa. Transformation of quantum states using uniformly controlled rotations. 2004. arXiv:quant-ph/0407010.

28

Pennylane. Momentum optimizer. URL: https://docs.pennylane.ai/en/stable/code/api/pennylane.MomentumOptimizer.html.

29

Pennylane. Nesterov momentum optimizer. URL: https://docs.pennylane.ai/en/stable/code/api/pennylane.NesterovMomentumOptimizer.html.

30

Adrián Pérez-Salinas, Alba Cervera-Lierta, Elies Gil-Fuster, and José I. Latorre. Data re-uploading for a universal quantum classifier. Quantum, 4:226, February 2020. URL: http://dx.doi.org/10.22331/q-2020-02-06-226, doi:10.22331/q-2020-02-06-226.

31

Qibo. Qibo. URL: https://qibo.science/.

32

Qiskit. Quantum machine learning. URL: Qiskit/textbook.

33

qm-ware. Qmware. URL: https://www.qm-ware.com/.

34

Maria Schuld. Kernel-based training of quantum models with scikit-learn. URL: https://pennylane.ai/qml/demos/tutorial_kernel_based_training.html.

35

Maria Schuld. Supervised quantum machine learning models are kernel methods. arXiv preprint arXiv:2101.11020, 2021.

36

Maria Schuld and Nathan Killoran. Quantum machine learning in feature hilbert spaces. Physical Review Letters, February 2019. URL: http://dx.doi.org/10.1103/PhysRevLett.122.040504, doi:10.1103/physrevlett.122.040504.

37

Maria Schuld and Nathan Killoran. Quantum machine learning in feature hilbert spaces. Phys. Rev. Lett., 122:040504, Feb 2019. URL: https://link.aps.org/doi/10.1103/PhysRevLett.122.040504, doi:10.1103/PhysRevLett.122.040504.

38

scikit-learn. Support vector machines. URL: https://scikit-learn.org/stable/modules/svm.html#.

39

Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In International conference on machine learning, 1139‚Äď1147. PMLR, 2013.

40

Wikipedia. Broyden‚Äďfletcher‚Äďgoldfarb‚Äďshanno algorithm. URL: https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm.

41

Srinivasan Arunachalam Yunchao Liu and Kristan Temme. A rigorous and robust quantum speed-up in supervised machine learning. URL: https://people.eecs.berkeley.edu/~yunchaoliu/slides/quantumkernel_IBM.pdf.

42

Matthew D Zeiler. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701, 2012.