Southwest Quantum Information and Technology

Group Invariant Quantum Machine Learning

Presenting Author: Martin Larocca, Los Alamos National Laboratory
Contributing Author(s): Frederic Sauvage, Marco Cerezo, Guillaume Verdon, Faris Sbahi, Patrick Coles, Marco Cerezo

Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data and task are used to build QML models that, by construction, respect those symmetries. Specifically, these group-invariant models produce outputs that remain fixed under the action of some symmetry group $\mathfrak{G}$ associated with the learning task. We first present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and then exemplify their application through several paradigmatic QML classification tasks. Notably, our framework allows us to recover, in an elegant way, several well known algorithms for the literature, as well as to discover new ones. Taken together, our results pave the way towards a more effective QML model design.

Read this article online: https://arxiv.org/abs/2205.02261

(Session 5 : Thursday from 5:00 pm - 7:00 pm)