Predicting fermionic densities using a Projected Quantum Kernel method

2025/04/18 by Perciavalle, Francesco, Plastina, Francesco, Pisarra, Michele +1 · 2 citations
#FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2504.14002

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.

Citations

• Physics-Informed Neural Networks for One-Dimensional Quantum Well Problems
• Paying attention to long-range electron correlation: a size-independent deep-learning approach to predicting molecules' electronic energies from one- and two-electron integrals
• Quantum reservoir computing for photonic entanglement witnessing
• Robust Quantum Reservoir Computing for Molecular Property Prediction
• Large-scale quantum reservoir learning with an analog quantum computer
• Quantum reservoir computing using arrays of Rydberg atoms
• Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays
• Dynamical Phase Transitions in Quantum Reservoir Computing
• Opportunities in Quantum Reservoir Computing and Extreme Learning Machines
• A concise review of Rydberg atom based quantum computation and quantum simulation*
• Quantum simulation and computing with Rydberg-interacting qubits
• Power of data in quantum machine learning
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum classifier with tailored quantum kernel
• Rydberg atom quantum technologies
• Treelike interactions and fast scrambling with cold atoms
• Machine learning and the physical sciences
• Boosting computational power through spatial multiplexing in quantum reservoir computing
• Probing many-body dynamics on a 51-atom quantum simulator
• QuantumOptics.jl: A Julia framework for simulating open quantum systems
• Quantum Machine Learning
• Local density approximations from finite systems
• Pure density functional for strong correlation and the thermodynamic limit from machine learning
• By-passing the Kohn-Sham equations with machine learning
• One Dimensional Mimicking of Electronic Structure: The Case for Exponentials
• Understanding density functional theory (DFT) and completing it in practice
• Chemistry in One Dimension
• Understanding Machine-learned Density Functionals
• Modeling techniques for quantum cascade lasers
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Orbital-free bond breaking via machine learning
• Reference electronic structure calculations in one dimension
• Perspective on density functional theory
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Scikit-learn: Machine Learning in Python
• Quantum Cascade Laser
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• Entanglement and Classical Simulability in Quantum Extreme Learning Machines
• Assessing Projected Quantum Kernels for the Classification of IoT Data

Related

• Understanding Machine-learned Density Functionals
• A Kernel-Based Density of States Estimator for Quantum Computing
• Direct Estimation of the Density of States for Fermionic Systems
• Inferring the quantum density matrix with machine learning
• Machine Learning Green's Functions of Strongly Correlated Hubbard Models