Abstract
Quantum Information Processing (QIP) performs wonders in a world that obeys the laws of quantum mechanics, whereas Machine Learning (ML) is generally assumed to be done in a classical world. We initiate an investigation of the encounter of ML with QIP by defining and studying novel learning tasks that correspond to Machine Learning in a world in which the information is fundamentally quantum mechanical. We shall see that this paradigm shift has a profound impact on the learning process and that our classical intuition is often challenged.
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References
Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)
Barenco, A., Berthiaume, A., Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C.: Stabilisation of quantum computations by symmetrisation. SIAM Journal of Computing 26(5), 1541–1557 (1997)
Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, pp. 175–179 (1984)
Buhrman, H., Cleve, R., Watrous, J., de Wolf, R.: Quantum fingerprinting. Physical Reviews Letters 87(16), article 167902 (2001)
Chiribella, G., Mauro D’Ariano, G., Perinotti, P., Sacchi, M.: Covariant quantum measurements which maximize the likelihood. Physical Reviews A 70, article 61205 (2004)
Ezhov, A.A., Berman, G.P.: Introduction to Quantum Neural Technologies. Rinton Press (2003)
Freund, Y., Shapire, R.: A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences 55(1), 119–139 (1997)
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters 79, 325–328 (1997)
Hayashi, A., Hashimoto, T., Horibe, M.: Reexamination of optimal quantum state estimation of pure states. Physical Reviews A 72, article 32325 (2005)
Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, London (1976)
Herzog, U., Bergou, J.A.: Optimal unambiguous discrimination of two mixed quantum states. Physical Reviews A 71, article 50301 (2005)
Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum mechanical channel. Problems of Information Transmissions 9, 177–183 (1973)
Horn, D., Gottlieb, A.: The method of quantum clustering. In: Proceedings of the Conference Neural Information Processing Systems (NIPS), pp. 769–776 (2001)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Peres, A., Wootters, W.K.: Optimal detection of quantum information. Physical Reviews Letters 66(9), 1119–1122 (1991)
Quinlan, J.R.: Induction of decision trees. Machine Learning 1, 81–106 (1986)
Sasaki, M., Carlini, A.: Quantum learning and universal quantum matching machine. Physical Reviews A 66(2), article 22303 (2002)
Sen, P.: Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. In: Proceedings of 21st Annual IEEE Conference on Computational Complexity (CCC) (to appear, 2006)
Servedio, R.: Separating quantum and classical learning. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, Springer, Heidelberg (2001)
Servedio, R., Gortler, A.: Equivalences and separations between quantum and classical learnability. SIAM Journal of Computing 33(5), 1067–1092 (2004)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal of Computing 26, 1484–1509 (1997)
Valiant, L.G.: A theory of the learnable. Communications of the ACM 27, 1134–1142 (1984)
Wootters, W.K., Zurek, W.C.: A single quantum cannot be cloned. Nature 66, 802–803 (1982)
Ziman, M., Plesch, M., Bužek, V., Štelmachovič, P.: Process reconstruction: From unphysical to physical maps via maximum likelihood. Physical Reviews A 71, article 22106 (2005)
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Aïmeur, E., Brassard, G., Gambs, S. (2006). Machine Learning in a Quantum World. In: Lamontagne, L., Marchand, M. (eds) Advances in Artificial Intelligence. Canadian AI 2006. Lecture Notes in Computer Science(), vol 4013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11766247_37
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DOI: https://doi.org/10.1007/11766247_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34628-9
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