Variational quantum algorithms, when a parametrized quantum circuit (PQC) is optimized by a classical algorithm to solve a specific problem, are expected to be the leading candidate for near-term quantum advantage. These hybrid quantum-classical algorithms can be applied in a variety of contexts, and there is hope that their hybrid nature can make them robust to noise to some degree.
When training a PQC in this setting to solve a specific problem, the right choice of circuit structure, also known as the ansatz, is of key importance the trainability and performance of the algorithm. For quantum machine learning however, it is largely unknown which type of ansatz should be used for a given type of data.
In this work, EQUALITY partners from Leiden University and collaborators introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations.
The authors 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. They analytically and numerically study the performance of the model, and their results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.
This work motivates further study of “geometric quantum learning” in the vein of the classical field of geometric deep learning, to establish more effective ansatzes for QML, as these are a pre-requisite to efficiently apply quantum models on any practically relevant learning task in the near-term.
Read the paper by clicking on the link below.
