Predicting fermionic densities using a projected-quantum-kernel method

We use support vector regression based on a projected-quantum-kernel method to predict the density structure of one-dimensional fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built upon with the observables of a quantum reservoir implementable with interacting Rydberg atoms. Training and test data of the fermionic system are generated using a density-functional theory approach. We test the performance of the method for several Hamiltonian parameters, finding a general common behavior of the error as a function of measurement time. At sufficiently long measurement times, we find that the method outperforms the classical linear kernel method and becomes competitive with the radial basis function method.