Towards Sampling from Nondirected Probabilistic Graphical models using a D-Wave Quantum Annealer

by   Yaroslav Koshka, et al.

A D-Wave quantum annealer (QA) having a 2048 qubit lattice, with no missing qubits and couplings, allowed embedding of a complete graph of a Restricted Boltzmann Machine (RBM). A handwritten digit OptDigits data set having 8x7 pixels of visible units was used to train the RBM using a classical Contrastive Divergence. Embedding of the classically-trained RBM into the D-Wave lattice was used to demonstrate that the QA offers a high-efficiency alternative to the classical Markov Chain Monte Carlo (MCMC) for reconstructing missing labels of the test images as well as a generative model. At any training iteration, the D-Wave-based classification had classification error more than two times lower than MCMC. The main goal of this study was to investigate the quality of the sample from the RBM model distribution and its comparison to a classical MCMC sample. For the OptDigits dataset, the states in the D-Wave sample belonged to about two times more local valleys compared to the MCMC sample. All the lowest-energy (the highest joint probability) local minima in the MCMC sample were also found by the D-Wave. The D-Wave missed many of the higher-energy local valleys, while finding many "new" local valleys consistently missed by the MCMC. It was established that the "new" local valleys that the D-Wave finds are important for the model distribution in terms of the energy of the corresponding local minima, the width of the local valleys, and the height of the escape barrier.


page 4

page 6

page 7

page 8

page 9


Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphi...

Comparison of D-Wave Quantum Annealing and Classical Simulated Annealing for Local Minima Determination

Restricted Boltzmann Machines trained with different numbers of iteratio...

Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer

We present the application of Restricted Boltzmann Machines (RBMs) to th...

Provable Convergence of Variational Monte Carlo Methods

The Variational Monte Carlo (VMC) is a promising approach for computing ...

On Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models

In this work, we demonstrate that applying deep generative machine learn...

On the Challenges of Physical Implementations of RBMs

Restricted Boltzmann machines (RBMs) are powerful machine learning model...

Coreset of Hyperspectral Images on Small Quantum Computer

Machine Learning (ML) techniques are employed to analyze and process big...

Please sign up or login with your details

Forgot password? Click here to reset