Quantum machine learning: a classical perspective
暂无分享,去创建一个
Simone Severini | Andrea Rocchetto | Mark Herbster | Alessandro Davide Ialongo | Massimiliano Pontil | Carlo Ciliberto | Leonard Wossnig | M. Pontil | M. Herbster | S. Severini | C. Ciliberto | Andrea Rocchetto | L. Wossnig | Leonard Wossnig
[1] QUANTITATIVE STUDIES , 1967 .
[2] L. Csanky,et al. Fast parallel matrix inversion algorithms , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).
[3] J. Linnett,et al. Quantum mechanics , 1975, Nature.
[4] Elwyn R. Berlekamp,et al. On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.
[5] D. Heller. A Survey of Parallel Algorithms in Numerical Linear Algebra. , 1978 .
[6] J. Laurie Snell,et al. Markov Random Fields and Their Applications , 1980 .
[7] F. Barahona. On the computational complexity of Ising spin glass models , 1982 .
[8] László Lovász,et al. Submodular functions and convexity , 1982, ISMP.
[9] Gene H. Golub,et al. Matrix computations , 1983 .
[10] Leslie G. Valiant,et al. A theory of the learnable , 1984, STOC '84.
[11] Scott Kirkpatrick,et al. Optimization by simulated annealing: Quantitative studies , 1984 .
[12] Paul Smolensky,et al. Information processing in dynamical systems: foundations of harmony theory , 1986 .
[13] Yves Robert,et al. Complexity of parallel QR factorization , 1986, JACM.
[14] Don Coppersmith,et al. Matrix multiplication via arithmetic progressions , 1987, STOC.
[15] Dana Angluin,et al. Queries and concept learning , 1988, Machine Learning.
[16] J. G. Pierce,et al. Geometric Algorithms and Combinatorial Optimization , 2016 .
[17] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..
[18] Karsten A. Verbeurgt. Learning DNF under the uniform distribution in quasi-polynomial time , 1990, COLT '90.
[19] Gregory F. Cooper,et al. The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..
[20] L. Bottou. Stochastic Gradient Learning in Neural Networks , 1991 .
[21] Alistair Sinclair,et al. Algorithms for Random Generation and Counting: A Markov Chain Approach , 1993, Progress in Theoretical Computer Science.
[22] Alistair Sinclair. Markov chains and rapid mixing , 1993 .
[23] Umesh V. Vazirani,et al. Quantum complexity theory , 1993, STOC.
[24] Leslie G. Valiant,et al. Cryptographic Limitations on Learning Boolean Formulae and Finite Automata , 1993, Machine Learning: From Theory to Applications.
[25] Yishay Mansour,et al. Weakly learning DNF and characterizing statistical query learning using Fourier analysis , 1994, STOC '94.
[26] J. Shewchuk. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain , 1994 .
[27] Sampath Kannan,et al. Oracles and queries that are sufficient for exact learning (extended abstract) , 1994, COLT '94.
[28] Sampath Kannan,et al. Oracles and Queries That Are Sufficient for Exact Learning , 1996, J. Comput. Syst. Sci..
[29] Subhash C. Kak,et al. On Quantum Neural Computing , 1995, Inf. Sci..
[30] Nader H. Bshouty,et al. Learning DNF over the uniform distribution using a quantum example oracle , 1995, COLT '95.
[31] Christopher M. Bishop,et al. Current address: Microsoft Research, , 2022 .
[32] Lov K. Grover. A fast quantum mechanical algorithm for database search , 1996, STOC '96.
[33] David Bruce Wilson,et al. Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.
[34] J. Propp,et al. Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996 .
[35] Guozhong An,et al. The Effects of Adding Noise During Backpropagation Training on a Generalization Performance , 1996, Neural Computation.
[36] Gilles Brassard,et al. Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..
[37] Vladimir Vapnik,et al. Statistical learning theory , 1998 .
[38] Peter W. Shor,et al. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..
[39] Alexander Schrijver,et al. A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time , 2000, J. Comb. Theory B.
[40] M. Sipser,et al. Quantum Computation by Adiabatic Evolution , 2000, quant-ph/0001106.
[41] Edward Farhi,et al. A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability , 2000, ArXiv.
[42] B. Schölkopf,et al. Sparse Greedy Matrix Approximation for Machine Learning , 2000, ICML.
[43] G. Brassard,et al. Quantum Amplitude Amplification and Estimation , 2000, quant-ph/0005055.
[44] Christopher K. I. Williams,et al. Using the Nyström Method to Speed Up Kernel Machines , 2000, NIPS.
[45] Satoru Iwata,et al. A combinatorial strongly polynomial algorithm for minimizing submodular functions , 2001, JACM.
[46] Shai Ben-David,et al. Limitations of Learning Via Embeddings in Euclidean Half Spaces , 2003, J. Mach. Learn. Res..
[47] Rocco A. Servedio,et al. Learning DNF in time , 2001, STOC '01.
[48] Nando de Freitas,et al. An Introduction to Sequential Monte Carlo Methods , 2001, Sequential Monte Carlo Methods in Practice.
[49] Radford M. Neal. Annealed importance sampling , 1998, Stat. Comput..
[50] Felipe Cucker,et al. On the mathematical foundations of learning , 2001 .
[51] Sanjeev Khanna,et al. Complexity classifications of Boolean constraint satisfaction problems , 2001, SIAM monographs on discrete mathematics and applications.
[52] Nando de Freitas,et al. Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.
[53] Shang-Hua Teng,et al. Smoothed analysis of algorithms: why the simplex algorithm usually takes polynomial time , 2001, STOC '01.
[54] E. Farhi,et al. A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.
[55] Johan Håstad,et al. Some optimal inapproximability results , 2001, JACM.
[56] R. Xu,et al. Theory of open quantum systems , 2002 .
[57] I. Jolliffe. Principal Component Analysis , 2002 .
[58] Lov K. Grover,et al. Creating superpositions that correspond to efficiently integrable probability distributions , 2002, quant-ph/0208112.
[59] P. Moral,et al. Sequential Monte Carlo samplers , 2002, cond-mat/0212648.
[60] Geoffrey E. Hinton. Training Products of Experts by Minimizing Contrastive Divergence , 2002, Neural Computation.
[61] R. Jozsa,et al. On the role of entanglement in quantum-computational speed-up , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[62] Sean Hallgren,et al. Quantum algorithms for some hidden shift problems , 2003, SODA '03.
[63] Rocco A. Servedio,et al. Maximum Margin Algorithms with Boolean Kernels , 2005, J. Mach. Learn. Res..
[64] Nello Cristianini,et al. Learning the Kernel Matrix with Semidefinite Programming , 2002, J. Mach. Learn. Res..
[65] Alan M. Frieze,et al. Fast monte-carlo algorithms for finding low-rank approximations , 2004, JACM.
[66] Ben Reichardt,et al. The quantum adiabatic optimization algorithm and local minima , 2004, STOC '04.
[67] M. Szegedy,et al. Quantum Walk Based Search Algorithms , 2008, TAMC.
[68] Seth Lloyd,et al. Adiabatic quantum computation is equivalent to standard quantum computation , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.
[69] Rocco A. Servedio,et al. Equivalences and Separations Between Quantum and Classical Learnability , 2004, SIAM J. Comput..
[70] T. Lumley,et al. PRINCIPAL COMPONENT ANALYSIS AND FACTOR ANALYSIS , 2004, Statistical Methods for Biomedical Research.
[71] Andris Ambainis,et al. Coins make quantum walks faster , 2004, SODA '05.
[72] Vadim Lyubashevsky,et al. The Parity Problem in the Presence of Noise, Decoding Random Linear Codes, and the Subset Sum Problem , 2005, APPROX-RANDOM.
[73] Rocco A. Servedio,et al. Improved Bounds on Quantum Learning Algorithms , 2004, Quantum Inf. Process..
[74] Kilian Q. Weinberger,et al. Graph Laplacian Regularization for Large-Scale Semidefinite Programming , 2006, NIPS.
[75] H. Krovi,et al. Hitting time for quantum walks on the hypercube (8 pages) , 2005, quant-ph/0510136.
[76] Gerhard Weikum,et al. WWW 2007 / Track: Semantic Web Session: Ontologies ABSTRACT YAGO: A Core of Semantic Knowledge , 2022 .
[77] Lorenzo Rosasco,et al. On regularization algorithms in learning theory , 2007, J. Complex..
[78] Sanjeev Arora,et al. A combinatorial, primal-dual approach to semidefinite programs , 2007, STOC '07.
[79] Sean Hallgren. Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem , 2007, JACM.
[80] Radford M. Neal. Pattern Recognition and Machine Learning , 2007, Technometrics.
[81] Thierry Paul,et al. Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.
[82] Benjamin Recht,et al. Random Features for Large-Scale Kernel Machines , 2007, NIPS.
[83] Andrew McCallum,et al. Introduction to Statistical Relational Learning , 2007 .
[84] E. Knill,et al. Optimal quantum measurements of expectation values of observables , 2006, quant-ph/0607019.
[85] A. Caponnetto,et al. Optimal Rates for the Regularized Least-Squares Algorithm , 2007, Found. Comput. Math..
[86] Jeff A. Bilmes,et al. Local Search for Balanced Submodular Clusterings , 2007, IJCAI.
[87] Ben Reichardt,et al. Fault-Tolerant Quantum Computation , 2016, Encyclopedia of Algorithms.
[88] S. Lloyd,et al. Architectures for a quantum random access memory , 2008, 0807.4994.
[89] A. Young,et al. Size dependence of the minimum excitation gap in the quantum adiabatic algorithm. , 2008, Physical review letters.
[90] E. Knill,et al. Quantum simulations of classical annealing processes. , 2008, Physical review letters.
[91] Seth Lloyd,et al. Quantum random access memory. , 2007, Physical review letters.
[92] Jean-Philippe Vert,et al. Group lasso with overlap and graph lasso , 2009, ICML '09.
[93] Andris Ambainis,et al. The Need for Structure in Quantum Speedups , 2009, Theory Comput..
[94] Lance Fortnow,et al. The status of the P versus NP problem , 2009, CACM.
[95] Steve Mullett,et al. Read the fine print. , 2009, RN.
[96] Sanjeev Arora,et al. Computational Complexity: A Modern Approach , 2009 .
[97] Shang-Hua Teng,et al. Smoothed analysis: an attempt to explain the behavior of algorithms in practice , 2009, CACM.
[98] Carl E. Rasmussen,et al. Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.
[99] Tamara G. Kolda,et al. Tensor Decompositions and Applications , 2009, SIAM Rev..
[100] P. Wocjan,et al. Quantum algorithm for approximating partition functions , 2008, 0811.0596.
[101] Andrew M. Childs. Quantum algorithms: Equation solving by simulation , 2009 .
[102] James B. Orlin,et al. A faster strongly polynomial time algorithm for submodular function minimization , 2007, Math. Program..
[103] Song Li. Fast algorithms for sparse matrix inverse computations , 2009 .
[104] A. Harrow,et al. Quantum algorithm for linear systems of equations. , 2008, Physical review letters.
[105] D. Poulin,et al. Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer. , 2009, Physical review letters.
[106] H. Krovi,et al. Adiabatic condition and the quantum hitting time of Markov chains , 2010, 1004.2721.
[107] By W. R. GILKSt,et al. Adaptive Rejection Sampling for Gibbs Sampling , 2010 .
[108] Michael I. Jordan,et al. On the Consistency of Ranking Algorithms , 2010, ICML.
[109] Pawel Wocjan,et al. Quantum algorithm for preparing thermal Gibbs states - detailed analysis , 2010, Quantum Cryptography and Computing.
[110] Dave Bacon,et al. Recent progress in quantum algorithms , 2010, Commun. ACM.
[111] S. Boixo,et al. Preparing thermal states of quantum systems by dimension reduction. , 2010, Physical review letters.
[112] Chi Zhang,et al. An improved lower bound on query complexity for quantum PAC learning , 2010, Inf. Process. Lett..
[113] A. Young,et al. First-order phase transition in the quantum adiabatic algorithm. , 2009, Physical review letters.
[114] Rocco A. Servedio,et al. Restricted Boltzmann Machines are Hard to Approximately Evaluate or Simulate , 2010, ICML.
[115] Estevam R. Hruschka,et al. Toward an Architecture for Never-Ending Language Learning , 2010, AAAI.
[116] Search via Quantum Walk , 2006, SIAM J. Comput..
[117] Radford M. Neal. Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .
[118] Philipp Birken,et al. Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.
[119] Itay Hen,et al. Exponential Complexity of the Quantum Adiabatic Algorithm for certain Satisfiability Problems , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.
[120] Nando de Freitas,et al. Toward the Implementation of a Quantum RBM , 2011 .
[121] Misha Denil. Toward the Implementation of a Quantum RBM , 2011 .
[122] Yee Whye Teh,et al. Bayesian Learning via Stochastic Gradient Langevin Dynamics , 2011, ICML.
[123] Salil P. Vadhan,et al. Computational Complexity , 2005, Encyclopedia of Cryptography and Security.
[124] F. Verstraete,et al. Quantum Metropolis sampling , 2009, Nature.
[125] Nathan Halko,et al. Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions , 2009, SIAM Rev..
[126] B. Recht,et al. Tensor completion and low-n-rank tensor recovery via convex optimization , 2011 .
[127] Hui Lin,et al. A Class of Submodular Functions for Document Summarization , 2011, ACL.
[128] Eric Darve,et al. Extension and optimization of the FIND algorithm: Computing Green's and less-than Green's functions , 2011, J. Comput. Phys..
[129] Kevin P. Murphy,et al. Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.
[130] Martin Schwarz,et al. Preparing projected entangled pair states on a quantum computer. , 2011, Physical review letters.
[131] P. Shor,et al. Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs , 2012, 1208.3757.
[132] Geoffrey E. Hinton,et al. ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.
[133] Andris Ambainis,et al. Variable time amplitude amplification and quantum algorithms for linear algebra problems , 2012, STACS.
[134] Massimiliano Pontil,et al. A New Convex Relaxation for Tensor Completion , 2013, NIPS.
[135] B. D. Clader,et al. Preconditioned quantum linear system algorithm. , 2013, Physical review letters.
[136] Martin J. Wainwright,et al. Divide and Conquer Kernel Ridge Regression , 2013, COLT.
[137] Massimiliano Pontil,et al. Multilinear Multitask Learning , 2013, ICML.
[138] Johan A. K. Suykens,et al. Learning with tensors: a framework based on convex optimization and spectral regularization , 2014, Machine Learning.
[139] Christopher J. Hillar,et al. Most Tensor Problems Are NP-Hard , 2009, JACM.
[140] Scott Aaronson,et al. Quantum Computing since Democritus , 2013 .
[141] Andrea Montanari,et al. A statistical model for tensor PCA , 2014, NIPS.
[142] Anupam Prakash,et al. Quantum algorithms for linear algebra and machine learning , 2014 .
[143] Yoshua Bengio,et al. On the Challenges of Physical Implementations of RBMs , 2013, AAAI.
[144] Bo Huang,et al. Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery , 2013, ICML.
[145] E. Farhi,et al. A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem , 2014, 1412.6062.
[146] Yoshua Bengio,et al. Generative Adversarial Nets , 2014, NIPS.
[147] Anton van den Hengel,et al. Semidefinite Programming , 2014, Computer Vision, A Reference Guide.
[148] Maria Schuld,et al. The quest for a Quantum Neural Network , 2014, Quantum Information Processing.
[149] F. Petruccione,et al. An introduction to quantum machine learning , 2014, Contemporary Physics.
[150] Igor L. Markov,et al. Limits on fundamental limits to computation , 2014, Nature.
[151] Wei Zhang,et al. Knowledge vault: a web-scale approach to probabilistic knowledge fusion , 2014, KDD.
[152] E. Farhi,et al. A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.
[153] Matthew Day,et al. Advances in quantum machine learning , 2015, 1512.02900.
[154] Yin Tat Lee,et al. A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.
[155] Steven H. Adachi,et al. Application of Quantum Annealing to Training of Deep Neural Networks , 2015, ArXiv.
[156] Ashish Kapoor,et al. Quantum Inspired Training for Boltzmann Machines , 2015, ArXiv.
[157] Prasad Raghavendra,et al. Beating the random assignment on constraint satisfaction problems of bounded degree , 2015, Electron. Colloquium Comput. Complex..
[158] Anmer Daskin. Quantum Principal Component Analysis , 2015 .
[159] L. Rosasco,et al. Less is More: Nystr\"om Computational Regularization , 2015 .
[160] Andrew W. Cross,et al. Quantum learning robust against noise , 2014, 1407.5088.
[161] Quoc V. Le,et al. Adding Gradient Noise Improves Learning for Very Deep Networks , 2015, ArXiv.
[162] Ashley Montanaro,et al. Quantum algorithms: an overview , 2015, npj Quantum Information.
[163] Éva Tardos,et al. Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..
[164] Srinivasan Arunachalam,et al. On the Robustness of Bucket Brigade Quantum RAM , 2015, TQC.
[165] Lorenzo Rosasco,et al. Less is More: Nyström Computational Regularization , 2015, NIPS.
[166] Andrew M. Childs,et al. Quantum linear systems algorithm with exponentially improved dependence on precision , 2015 .
[167] Damian S. Steiger,et al. Racing in parallel: Quantum versus Classical , 2016 .
[168] Sergey Ioffe,et al. Rethinking the Inception Architecture for Computer Vision , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
[169] Krysta Marie Svore,et al. Quantum Speed-ups for Semidefinite Programming , 2016, ArXiv.
[170] Wojciech Zaremba,et al. Improved Techniques for Training GANs , 2016, NIPS.
[171] Demis Hassabis,et al. Mastering the game of Go with deep neural networks and tree search , 2016, Nature.
[172] Aram Wettroth Harrow,et al. Simulated Quantum Annealing Can Be Exponentially Faster Than Classical Simulated Annealing , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).
[173] Seth Lloyd,et al. Quantum algorithms for topological and geometric analysis of data , 2016, Nature Communications.
[174] M. Benedetti,et al. Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning , 2015, 1510.07611.
[175] Roger Melko,et al. Quantum Boltzmann Machine , 2016, 1601.02036.
[176] M. Schuld,et al. Prediction by linear regression on a quantum computer , 2016, 1601.07823.
[177] Rolando D. Somma,et al. Quantum algorithms for Gibbs sampling and hitting-time estimation , 2016, Quantum Inf. Comput..
[178] Ashish Kapoor,et al. Quantum deep learning , 2014, Quantum Inf. Comput..
[179] Robert Gardner,et al. Quantum generalisation of feedforward neural networks , 2016, npj Quantum Information.
[180] M. Benedetti,et al. Estimation of effective temperatures in a quantum annealer: Towards deep learning applications , 2016 .
[181] Vore,et al. Quantum Speed-ups for Semidefinite Programming , 2017 .
[182] Ronald de Wolf,et al. Guest Column: A Survey of Quantum Learning Theory , 2017, SIGA.
[183] H. Neven,et al. Quantum Algorithms for Fixed Qubit Architectures , 2017, 1703.06199.
[184] Ronald de Wolf,et al. A Survey of Quantum Learning Theory , 2017, ArXiv.
[185] Iordanis Kerenidis,et al. Quantum Recommendation Systems , 2016, ITCS.
[186] Ronald de Wolf,et al. Quantum SDP-Solvers: Better Upper and Lower Bounds , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).
[187] Ronald de Wolf,et al. Optimal Quantum Sample Complexity of Learning Algorithms , 2016, CCC.
[188] Alán Aspuru-Guzik,et al. Quantum autoencoders for efficient compression of quantum data , 2016, 1612.02806.
[189] Andrew M. Childs,et al. Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision , 2015, SIAM J. Comput..
[190] L. Wossnig,et al. Quantum Linear System Algorithm for Dense Matrices. , 2017, Physical review letters.
[191] Francis Bach,et al. Submodular functions: from discrete to continuous domains , 2015, Mathematical Programming.
[192] Iordanis Kerenidis,et al. Learning with Errors is easy with quantum samples , 2017, Physical Review A.
[193] Joseph Fitzsimons,et al. Quantum assisted Gaussian process regression , 2015, Physical Review A.
[194] Ievgeniia Oshurko. Quantum Machine Learning , 2020, Quantum Computing.