Toward the Implementation of a Quantum RBM

Quantum computers promise the ability to solve many types of difficult computational problems efficiently. It turns out that Boltzmann Machines are ideal candidates for implementation on a quantum computer, due to their close relationship to the Ising model from statistical physics. In this paper we describe how to use quantum hardware to train Boltzmann Machines with connections between latent units. We also describe the architecture we are targeting and discuss difficulties we face in applying the current generation of quantum computers to this hard problem.

[1]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[2]  Thomas Kailath,et al.  Model-free distributed learning , 1990, IEEE Trans. Neural Networks.

[3]  Marwan A. Jabri,et al.  Weight Perturbation: An Optimal Architecture and Learning Technique for Analog VLSI Feedforward and Recurrent Multilayer Networks , 1991, Neural Comput..

[4]  Gert Cauwenberghs,et al.  A Fast Stochastic Error-Descent Algorithm for Supervised Learning and Optimization , 1992, NIPS.

[5]  Ron Meir,et al.  A Parallel Gradient Descent Method for Learning in Analog VLSI Neural Networks , 1992, NIPS.

[6]  Gert Cauwenberghs A Learning Analog Neural Network Chip with Continuous-Time Recurrent Dynamics , 1993, NIPS.

[7]  Adnan Darwiche,et al.  Inference in belief networks: A procedural guide , 1996, Int. J. Approx. Reason..

[8]  Rosenbaum,et al.  Quantum annealing of a disordered magnet , 1999, Science.

[9]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[10]  M. Amin The effect of local minima on quantum adiabatic optimization , 2007 .

[11]  James C. Spall,et al.  Introduction to Stochastic Search and Optimization. Estimation, Simulation, and Control (Spall, J.C. , 2007 .

[12]  Geoffrey E. Hinton,et al.  Modeling image patches with a directed hierarchy of Markov random fields , 2007, NIPS.

[13]  J. Biamonte,et al.  Realizable Hamiltonians for Universal Adiabatic Quantum Computers , 2007, 0704.1287.

[14]  M. Amin,et al.  Effect of local minima on adiabatic quantum optimization. , 2007, Physical review letters.

[15]  Seth Lloyd,et al.  Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation , 2008, SIAM Rev..

[16]  R. Salakhutdinov Learning and Evaluating Boltzmann Machines , 2008 .

[17]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[18]  Sven Behnke,et al.  Exploiting local structure in stacked Boltzmann machines , 2010, ESANN.

[19]  Nando de Freitas,et al.  Inductive Principles for Restricted Boltzmann Machine Learning , 2010, AISTATS.

[20]  Dario Tamascelli,et al.  An introduction to quantum annealing , 2011, RAIRO Theor. Informatics Appl..

[21]  M. W. Johnson,et al.  Quantum annealing with manufactured spins , 2011, Nature.