  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.

Quantum Physics;Machine Learning