Radhakrishnan Balu

Noah A. Crum, Leanto Sunny, Pooya Ronagh et al.

Motivated by applications of quantum computers in Gibbs sampling from continuous real-valued functions, we ask whether such algorithms can provide practical advantages for machine learning models trained on classical data and seek measures for quantifying such impacts. In this study, we focus on deep energy-based models (EBM), as they require continuous-domain Gibbs sampling both during training and inference. In lieu of fault-tolerant quantum computers that can execute quantum Gibbs sampling algorithms, we use the Monte Carlo simulation of diffusion processes as a classical alternative. More specifically, we investigate whether long-run persistent chain Monte Carlo simulation of Langevin dynamics improves the quality of the representations achieved by EBMs. We consider a scheme in which the Monte Carlo simulation of a diffusion, whose drift is given by the gradient of the energy function, is used to improve the adversarial robustness and calibration score of an independent classifier network. Our results show that increasing the computational budget of Gibbs sampling in persistent contrastive divergence improves both the calibration and adversarial robustness of the model, suggesting a prospective avenue of quantum advantage for generative AI using future large-scale quantum computers.

Radhakrishnan Balu, Ajinkya Borle

We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of the nodes consistent with a given dataset. This is a combinatorial problem of structural learning of the underlying graph, starting from a single node and building one arc at a time, that fits a given ensemble using maximum likelihood estimators (MLE). It is cast as an optimization problem that consists of a scoring step performed on a classical computer, penalties for acyclicity and number of parents allowed constraints, and a search step implemented using a quantum annealer. We have assumed uniform priors in deriving the Bayesian network that can be relaxed by formulating the problem as an estimation Dirichlet parameters. We demonstrate the utility of the framework by applying to the problem of elucidating the gene regulatory network for the MAPK/Raf pathway in human T-cells using proteomics data where the concentration of proteins, nodes of the BN, are interpreted as probabilities.