Equivariant quantum circuits for learning on weighted graphs

arXiv (Cornell University)

Abstract

Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.

Authors 5

1. Andrea Skolik Aachen

   Leiden University · Volkswagen Group (Germany) · Volkswagen Group (United States)

   Affiliation as printed

   Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands

   Volkswagen Data:Lab , Ungererstraße 69 , 80805 Munich , Germany

2. Michele Cattelan

   Volkswagen Group (Germany) · Universität Innsbruck · Volkswagen Group (United States)

   Affiliation as printed

   Institute for Theoretical Physics , University of Innsbruck , A-6020 Innsbruck , Austria

   Volkswagen Data:Lab , Ungererstraße 69 , 80805 Munich , Germany

3. Sheir Yarkoni Aachen

   Leiden University · Volkswagen Group (Germany) · Volkswagen Group (United States)

   Affiliation as printed

   Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands

   Volkswagen Data:Lab , Ungererstraße 69 , 80805 Munich , Germany

4. Thomas Bäck Aachen

   Leiden University

   Affiliation as printed

   Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands

5. Vedran Dunjko Aachen

   Leiden University

   Affiliation as printed

   Leiden University , Niels Bohrweg 1 , 2333 CA Leiden , The Netherlands