Is Mode Connectivity Explainable by LOCC Equivalence

Alexandra Ballow, Montana State University

Photo of Alexandra Ballow

In the past decade, the field of deep learning has become incredibly successful in training large neural networks. Yet there remain many open questions about how and what these models are learning, and how that learning may change on a quantum computer. There are several open questions pertaining to the structure of solutions: where minima (corresponding to well-trained models that generalize to new data) sit, how they are shaped, and their connectivity. If minima are connected, understanding the mathematical reason for their connection could allow for easy detection of low loss paths between minima, leading to efficient implementations of geometric ensembles of quantum circuit models. Better understanding the interconnectivity in the lower dimensional landscapes can also assist in discovering new circuit ansatz families that are amenable to QML tasks, and perhaps more robust against barren plateaus. In this study we focus on graph states and how the relationship between two graphs can influence the connectivity between their respective minima. Specifically we look to show that Local Compliment (LC) equivalence of graph states corresponds to connected minima in the loss landscape. One approach taken to accomplish this goal is treating parameterized quantum circuits as Morse functions.

Abstract Author(s): Alexandra Ballow, Kathleen Hamilton