# Predicting fermionic densities using a Projected Quantum Kernel method

arXiv: https://arxiv.org/abs/2504.14002 · HTML: https://mlsanity.com/paper/2504.14002/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 67 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [Orbital-free Bond Breaking via Machine Learning](https://mlsanity.com/paper/1306.1812/) (2013)
- [Understanding Machine-learned Density Functionals](https://mlsanity.com/paper/1404.1333/) (2014)

## Abstract (arXiv)

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.