Comparison of Use of a 2000 Qubit D-Wave Quantum Annealer and MCMC for Sampling, Image Reconstruction, and Classification

Abstract

The next generation D-Wave quantum computer (QC) having more than 2000 qubits was demonstrated to be adequate for embedding graphs of restricted Boltzmann machines (RBMs) having the connectivity between RBM units (though still limited) already sufficient for successful training by classical algorithms. As a verification of the validity and quality of the employed embedding approach, the RBM was trained by classical contrastive divergence (CD), while the D-Wave was initially used only in the recognition step for reconstruction of incomplete test images (8 × 8 bars-and-stripes), and for their classification. The label classification errors by the D-Wave compared favorably to those obtained by classical Gibbs sampling, indicating that the QC was successfully finding the most energetically favorable combinations of the unknown visible RBM units/labels for the given fixed incomplete input image. The valid RBM embedding was further applied to investigate opportunities for using QCs in the RBM training, and specifically for replacing the classical Gibbs technique in generating a representative sample from the RBM model distribution. Statistical comparison of samples obtained by the Gibbs technique versus 10000 sample states generated from the D-Wave revealed significant differences in the observed outcomes. The D-Wave samples were found insufficiently representative of the model distribution, specifically by missing many local valley found by the Gibbs sampling. On the other hand, the D-Wave possessed an ability to find local valleys of the configuration space that were consistently missed by the classical sampling algorithms, which could potentially be very interesting for sampling applications.