Structural Modifications in Quantum-Assisted Training for General Boltzmann Machines

Quantum-assisted training of machine learning models makes use of the sampling capabilities of quantum computing devices to approximate the probability distribution of classical generative machine learning models. One example of this is the use of quantum annealers to sample from a Boltzmann distribution to assist the computation of gradients required to train Boltzmann machines (BMs). Doing so requires the interactions and weights of a BM to be mapped onto the underlying qubit connectivity built into the quantum device hardware. This opens the possibility of formulating any graph topology as a BM, instead of the more common classical approach of restricting their connectivity; i.e., Restricted Boltz-mann Machine (RBM). This work is focused on simultaneous modifications of the connectivity and qubit mapping of general BMs, which we refer to as structure-aware minor-embedding. We show how minor-embedding can be performed taking into account the nature of the BM. We also evaluate weight “pruning”, which is motivated by the intuition that, when a QAML model is pruned, the resulting qubit chains resulting from the minor-embedding methods can provide better quality samples, at the expense of a smaller model.