Predicting fermionic densities using a Projected Quantum Kernel method
This addresses quantum chemistry and matter problems, but appears incremental as it builds on existing quantum kernel approaches with specific performance comparisons.
The paper tackles predicting fermionic densities in 1D systems using a projected quantum kernel method with a support vector regressor, finding that at large measurement times, it outperforms classical linear kernels and is competitive with radial basis function methods.
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.