A quantum machine learning algorithm based on generative models

We propose a quantum learning algorithm for a quantum generative model and prove its advantages compared with classical models. Quantum computing and artificial intelligence, combined together, may revolutionize future technologies. A significant school of thought regarding artificial intelligence is based on generative models. Here, we propose a general quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is more capable of representing probability distributions compared with classical generative models and has exponential speedup in learning and inference at least for some instances if a quantum computer cannot be efficiently simulated classically. Our result opens a new direction for quantum machine learning and offers a remarkable example where a quantum algorithm shows exponential improvement over classical algorithms in an important application field.

[1]  Elham Kashefi,et al.  On the implausibility of classical client blind quantum computing , 2017, ArXiv.

[2]  S. Lloyd,et al.  Architectures for a quantum random access memory , 2008, 0807.4994.

[3]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[4]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[5]  Barbara M. Terhal,et al.  The complexity of quantum spin systems on a two-dimensional square lattice , 2008, Quantum Inf. Comput..

[6]  Xiaodi Wu,et al.  Quantum SDP Solvers: Large Speed-Ups, Optimality, and Applications to Quantum Learning , 2017, ICALP.

[7]  Krysta Marie Svore,et al.  Quantum Speed-Ups for Solving Semidefinite Programs , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[8]  Frank Verstraete,et al.  Peps as unique ground states of local hamiltonians , 2007, Quantum Inf. Comput..

[9]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[10]  Nicolas Le Roux,et al.  Representational Power of Restricted Boltzmann Machines and Deep Belief Networks , 2008, Neural Computation.

[11]  Anmer Daskin Quantum Principal Component Analysis , 2015 .

[12]  Seth Lloyd,et al.  Quantum random access memory. , 2007, Physical review letters.

[13]  White,et al.  Sign problem in the numerical simulation of many-electron systems. , 1990, Physical review. B, Condensed matter.

[14]  R. Feynman Simulating physics with computers , 1999 .

[15]  L. Duan,et al.  Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model. , 2016, Physical review letters.

[16]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..

[17]  C. Zu,et al.  Experimental demonstration of a quantum router , 2015, Scientific Reports.

[18]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[19]  Steve Mullett,et al.  Read the fine print. , 2009, RN.

[20]  Shai Ben-David,et al.  Understanding Machine Learning: From Theory to Algorithms , 2014 .

[21]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

[22]  Luming Duan,et al.  Quantum discriminant analysis for dimensionality reduction and classification , 2015, 1510.00113.

[23]  Yong Zhang,et al.  Fast amplification of QMA , 2009, Quantum Inf. Comput..

[24]  Martin Schwarz,et al.  Preparing projected entangled pair states on a quantum computer. , 2011, Physical review letters.

[25]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[26]  S. Lloyd,et al.  Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors , 1998, quant-ph/9807070.

[27]  S. Lloyd,et al.  Quantum algorithms for supervised and unsupervised machine learning , 2013, 1307.0411.

[28]  Ievgeniia Oshurko Quantum Machine Learning , 2020, Quantum Computing.

[29]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[30]  R. Cleve,et al.  Efficient Quantum Algorithms for Simulating Sparse Hamiltonians , 2005, quant-ph/0508139.

[31]  Simone Severini,et al.  Quantum machine learning: a classical perspective , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[32]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[33]  Julia Kempe,et al.  The Complexity of the Local Hamiltonian Problem , 2004, FSTTCS.

[34]  Roger Melko,et al.  Quantum Boltzmann Machine , 2016, 1601.02036.

[35]  Krysta Marie Svore,et al.  Quantum Speed-ups for Semidefinite Programming , 2016, ArXiv.

[36]  Seth Lloyd,et al.  Quantum algorithm for data fitting. , 2012, Physical review letters.

[37]  A. Harrow,et al.  Quantum algorithm for linear systems of equations. , 2008, Physical review letters.

[38]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.