2000 Qubit D-Wave Quantum Computer Replacing MCMC for RBM Image Reconstruction and Classification

Restricted Boltzmann Machines trained by the classical Contrastive Divergence algorithm were embedded into a next generation D-Wave quantum computer having more than 2000 qubits. The embedding was used to sample missing visible units and labels of incomplete test images. The previously introduced RBM embedding that combined qubits into individual RBM units in order to increase the connectivity between units was used. In comparison to the 1000 qubit machine investigated earlier, the same embedding approach applied to the 2000 qubit D-Wave enabled a connectivity between RBM units sufficient for RBM training on a classical computer with a satisfactory classification error. After a varied number of CD training iterations, the visible units corresponding to a particular incomplete test image were fixed in the D-Wave embedding. The resulting state returned by the D-Wave represents the most energetically favorable combination of the remaining qubits for the given fixed incomplete input image. The classification errors compared favorably to those obtained by the classical MCMC sampling. Main factors influencing the quality of the embedding were investigated. Regardless of the computational cost incentives for using the D-Wave for this operation, the reconstruction and classification errors determined in this way can be used at least as a verification of the validity and quality of the particular embedding of the given RBM architecture. This is essential for successfully employing a QC in much more computationally demanding parts of the RBM training. opportunities for using QC not only for recognition but especially for RBM training, in particular for obtaining a representative sample from the RBM model distribution, are discussed.