  Quantum computing can empower machine learning models by enabling kernel
machines to leverage quantum kernels for representing similarity measures
between data. Quantum kernels are able to capture relationships in the data
that are not efficiently computable on classical devices. However, there is no
straightforward method to engineer the optimal quantum kernel for each specific
use case. While recent literature has focused on exploiting the potential
offered by the presence of symmetries in the data to guide the construction of
quantum kernels, we adopt here a different approach, which employs optimization
techniques, similar to those used in neural architecture search and AutoML, to
automatically find an optimal kernel in a heuristic manner. The algorithm we
present constructs a quantum circuit implementing the similarity measure as a
combinatorial object, which is evaluated based on a cost function and is then
iteratively modified using a meta-heuristic optimization technique. The cost
function can encode many criteria ensuring favorable statistical properties of
the candidate solution, such as the rank of the Dynamical Lie Algebra.
Importantly, our approach is independent of the optimization technique
employed. The results obtained by testing our approach on a high-energy physics
problem demonstrate that, in the best-case scenario, we can either match or
improve testing accuracy with respect to the manual design approach, showing
the potential of our technique to deliver superior results with reduced effort.
