Predicting fermionic densities using a Projected Quantum Kernel method

We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on 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 large measurement times, we find that the method outperforms the classical linear kernel method and can be competitive with the radial basis function method.

@article{perciavalle2025_2504.14002,
  title={ Predicting fermionic densities using a Projected Quantum Kernel method },
  author={ Francesco Perciavalle and Francesco Plastina and Michele Pisarra and Nicola Lo Gullo },
  journal={arXiv preprint arXiv:2504.14002},
  year={ 2025 }
}