Quantum adiabatic machine learning

Kristen L. Pudenz1, Daniel A. Lidar1
1Department of Electrical Engineering, Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, USA

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Vapnik, V.N.: Statistical Learning Theory. Wiley, London (1998)

Servedio, R.A., Gortler, S.J.: Equivalences and separations between quantum and classical learnability. SIAM J. Comput. 33, 1067 (2004)

Aïmeur, E., Brassard, G., Gambs, S.: Machine learning in a quantum world. In: Lamontagne, L., Marchand, M. (eds.) Advances in Artificial Intelligence, vol. 4013 of Lecture Notes in Computer Science, p. 431. Springer, Berlin (2006)

Meir, R., Rätsch, G.: An introduction to boosting and leveraging. In: Mendelson, S., Smola, A. (eds.) Advanced Lectures on Machine Learning, vol. 2600 of Lecture Notes in Computer Science, p. 118. Springer, Berlin (2003)

Freund, Y., Schapire, R., Abe, N.: A short introduction to boosting. J. Jpn. Soc. Artif. Intell. 14, 771 (1999)

Neven, H., Denchev, V.S., Rose, G., Macready, W.G.: Training a binary classifier with the quantum adiabatic algorithm. eprint arXiv:0811.0416

Neven, H., Denchev., V.S., Drew-Brook, M., Zhang, J., Macready, W.G., Rose, G.: NIPS 2009 demonstration: Binary classification using hardware implementation of quantum annealing (2009)

Chandola, V., Banerjee, A., Kumar, V.: Anomaly detection: A survey. ACM Comput. Surv. (CSUR) 41(3), 15 (2009)

Dijkstra, E.W.: Notes on structured programming. In: Dahl, O.-J., Dijkstra, E.W., Hoare, C.A.R. (eds.) Structured Programming, p. 1. Academic Press, New York (1972)

Tassey, G.: The economic impacts of inadequate infrastructure for software testing. National Institute of Standards and Technology, RTI Project 7007.011 (2002)

Bryce, R., Kuhn, R., Lei, Y., Kacker, R.: Combinatorial testing. In: Ramachandran, M., de Carvalho, R.A. (eds.) Handbook of Software Engineering Research and Productivity Technologies, p. 196. IGI Global (2009)

Kuhn, D.R., Kacker, R.N., Lei, Y.: Practical combinatorial testing. NIST Special, Publication 800–142 (2010)

Grindal, M., Offutt, J., Andler, S.F.: Combination Testing Strategies: A survey. GMU Technical, Report ISE-TR-04-05 (2004)

Cohen, D.M., Dalal, S.R., Parelius, J., Patton, G.C.: The combinatorial design approach to automatic test generation. Softw. IEEE 13, 83 (1996)

D’Silva, V., Kroening, D., Weissenbacher, G.: A survey of automated techniques for formal software verification. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27, 1165 (2008)

Weber, T., Amjad, H.: Efficiently checking propositional refutations in HOL theorem provers. J. Appl. Log. 7, 26 (2009)

Neven, H., Rose, G., Macready, W.G.: Image recognition with an adiabatic quantum computer I. mapping to quadratic unconstrained binary optimization. eprint arXiv:0804.4457

Neven, H., Denchev, V.S., Rose, G., Macready, W.G.: Training a large scale classifier with the quantum adiabatic algorithm. eprint arXiv:0912.0779

Bian, Z., Chudak, F., Macready, W.G., Rose, G.: The Ising model: teaching an old problem new tricks. D-Wave Systems (2010)

Schapire, R.E.: The strength of weak learnability. Mach. Learn. 5, 197 (1990)

Farhi, E., Goldstone, J., Gutmann, S., Sipser, M.: Quantum computation by adiabatic evolution. eprint quant-ph/0001106

Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472 (2001)

Aharonov, D., van Dam, W., Kempe, J., Landau, Z., Lloyd, S., Regev, O.: Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J. Comput. 37, 166 (2007)

Mizel, A., Lidar, D.A., Mitchell, M.: Simple proof of equivalence between adiabatic quantum computation and the circuit model. Phys. Rev. Lett. 99, 070502 (2007)

Jordan, S.P., Farhi, E., Shor, P.W.: Error-correcting codes for adiabatic quantum computation. Phys. Rev. A 74, 052322 (2006)

Lidar, Daniel A.: Towards fault tolerant adiabatic quantum computation. Phys. Rev. Lett. 100, 160506 (2008)

Childs, Andrew M., Edward, Farhi, John, Preskill: Robustness of adiabatic quantum computation. Phys. Rev. A 65, 012322 (2001)

Sarandy, M.S., Lidar, D.A.: Adiabatic quantum computation in open systems. Phys. Rev. Lett. 95, 250503 (2005)

Stehle, E., Lynch, K., Shevertalov, M., Rorres, C., Mancoridis, S.: On the use of computational geometry to detect software faults at runtime. ICAC10, June 711. Washington, DC, USA (2010)

Le Traon, Y., Baudry, B., Jezequel, J.-M.: Design by contract to improve software vigilance. IEEE Trans. Softw. Eng. 32, 571 (2006)

Mannor, S., Meir, R.: Geometric bounds for generalization in boosting. In: Helmbold, D., Williamson, B. (eds.) Computational Learning Theory, vol. 2111 of Lecture Notes in Computer Science, pp. 461–472. Springer, Berlin (2001)

Kotsiantis, S.B.: Supervised machine learning: A review of classification techniques. Informatica 31, 249 (2007)

Yu, L., Liu, H.: Efficient feature selection via analysis of relevance and redundancy. J. Mach. Learn. Res. 5, 1205 (2004)

Zhang, S., Zhang, C., Yang, Q.: Data preparation for data mining. Appl. Artif. Intell. 17, 375 (2003)

Cheng, H., Yan, X., Han, J., Hsu, C.-W.: Discriminative frequent pattern analysis for effective classification. In: International Conference on Data Engineering, p. 716 (2007)

Breiman, L.: Arcing classifiers. Ann. Stat. 26, 801 (1998)

Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.K.: Occam’s razor. Inf. Process. Lett. 24, 377 (1987)

Biamonte, J.D., Peter, Love: Realizable Hamiltonians for universal adiabatic quantum computers. Phys. Rev. A 78, 012352 (2008)

Choi, V.: Minor-embedding in adiabatic quantum computation: I. The parameter setting problem. Quantum Inf. Process. 7, 193 (2008)

Karimi, K., Dickson, N.G., Hamze, F., Amin, M.H.S., Drew-Brook, M., Chudak, F.A., Bunyk, P.I., Macready, W.G., Rose, G.: Investigating the performance of an adiabatic quantum optimization processor. Quantum Inf. Process. 11(1), 77 (2012)

Harris, R., Johnson, M.W., Lanting, T., Berkley, A.J., Johansson, J., Bunyk, P., Tolkacheva, E., Ladizinsky, E., Ladizinsky, N., Oh, T., Cioata, F., Perminov, I., Spear, P., Enderud, C., Rich, C., Uchaikin, S., Thom, M.C., Chapple, E.M., Wang, J., Wilson, B., Amin, M.H.S., Dickson, N., Karimi, K., Macready, W., Truncik, C.J.S., Rose, G.: Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor. Phys. Rev. B 82, 024511 (2010)

Cheng, H., Yan, X., Han, J., Hsu, C.-W.: Discriminative frequent pattern analysis for effective classification. In: IEEE 23rd International Conference on Data Engineering, Istanbul, Turkey (2007)

Teufel, S.: Adiabatic Perturbation Theory in Quantum Dynamics. Springer, Berlin (2003)

Jansen, S., Ruskai, M.-B., Seiler, R.: Bounds for the adiabatic approximation with applications to quantum computation. J. Math. Phys. 48, 102111 (2007)

Lidar, D.A., Rezakhani, A.T., Hamma, A.: Adiabatic approximation with exponential accuracy for many-body systems and quantum computation. J. Math. Phys. 50, 102106 (2009)

Roland, J., Cerf, N.J.: Quantum search by local adiabatic evolution. Phys. Rev. A 65, 042308 (2002)

Rezakhani, A.T., Pimachev, A.K., Lidar, D.A.: Accuracy versus run time in an adiabatic quantum search. Phys. Rev. A 82, 052305 (2010)

Young, A.P., Knysh, S., Smelyanskiy, V.N.: Size dependence of the minimum excitation gap in the quantum adiabatic algorithm. Phys. Rev. Lett. 101, 170503 (2008)

Slepian, D.: On the number of symmetry types of Boolean functions of N variables. Can. J. Math. 5, 185 (1953)

Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C–35, 677 (1986)

Jordan, Stephen P., Edward, Farhi: Perturbative gadgets at arbitrary orders. Phys. Rev. A 77, 062329 (2008)

Rezakhani, A.T., Kuo, W.-J., Hamma, A., Lidar, D.A., Zanardi, P.: Quantum adiabatic brachistochrone. Phys. Rev. Lett. 103, 080502 (2009)

Rezakhani, A.T., Abasto, D.F., Lidar, D.A., Zanardi, P.: Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions. Phys. Rev. A 82, 012321 (2010)