Predicting fermionic densities using a Projected Quantum Kernel method

2025-04-18

AI Summary

This work addresses the high-accuracy prediction of electronic density profiles in one-dimensional fermionic systems. We propose a physics-informed machine learning approach based on experimentally realizable quantum kernels. Specifically, we construct a quantum reservoir from interacting Rydberg atoms and define a quantum kernel via projective measurements on this reservoir, which is then integrated with support vector regression (SVR) for density prediction. Our key contribution is the first incorporation of an experimentally feasible projective quantum kernel into data-driven density prediction within density functional theory (DFT). Extensive validation across multiple Hamiltonian parameter sets demonstrates that, under moderate measurement times, the proposed quantum kernel substantially outperforms classical linear kernels and approaches the performance of radial basis function (RBF) kernels. This establishes a novel paradigm for quantum-simulation-assisted quantum chemistry and modeling of strongly correlated materials.

Technology Category

• Machine Learning: Quantum Machine Learning
• Data Mining & Knowledge Management: Intelligent Query Processing
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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.

Problem

• Predict fermionic densities using quantum kernel method
• Compare performance with classical kernel methods
• Generate data via Density Functional Theory approach

Innovation

• Projected Quantum Kernel for fermionic densities
• Quantum reservoir with Rydberg atoms
• Outperforms classical linear kernel