Scalable Quantum Monte Carlo Method for Polariton Chemistry via Mixed Block Sparsity and Tensor Hypercontraction Method

Abstract

We present a reduced-scaling auxiliary-field quantum Monte Carlo (AFQMC) framework designed for large molecular systems and ensembles, with or without coupling to optical cavities. Our approach leverages the natural block sparsity of Cholesky decomposition (CD) of electron repulsion integrals in molecular ensembles and employs tensor hypercontraction (THC) to efficiently compress low-rank Cholesky blocks. By representing the Cholesky vectors in a mixed format, keeping high-rank blocks in block-sparse form and compressing low-rank blocks with THC, we reduce the scaling of exchange-energy evaluation from quartic to robust cubic in the number of molecular orbitals, while lowering memory from cubic toward quadratic. Benchmark analyses on one-, two-, and three-dimensional molecular ensembles (up to ~1,200 orbitals) show that: a) the number of nonzeros in Cholesky tensors grows linearly with system size across dimensions; b) the average numerical rank increases sublinearly and does not saturate at these sizes; and (c) rank heterogeneity-some blocks nearly full rank and many low rank, naturally motivating the proposed mixed block sparsity and THC scheme for efficient calculation of exchange energy. We demonstrate that the mixed scheme yields cubic CPU-time scaling with favorable prefactors and preserves AFQMC accuracy.

References in corpus (15)

• Intermolecular interactions in optical cavities: an ab initio QED study
• Ultrafast imaging of polariton propagation and interactions
• Cavity-modulated ionization potentials and electron affinities from quantum electrodynamics coupled-cluster theory
• Molecular orbital theory in cavity QED environments
• Quantum-Electrodynamical Time-Dependent Density Functional Theory. I. A Gaussian Atomic Basis Implementation
• Cavity-Born-Oppenheimer Hartree-Fock Ansatz: Light-matter Properties of Strongly Coupled Molecular Ensembles
• Equation-of-motion cavity quantum electrodynamics coupled-cluster theory for electron attachment
• Enhanced diastereocontrol via strong light-matter interactions in an optical cavity
• Assessing the Effects of Orbital Relaxation and the Coherent-State Transformation in Quantum Electrodynamics Density Functional and Coupled-Cluster Theories
• Variational Lang-Firsov approach plus Møller-Plesset perturbation theory with applications to ab initio polariton chemistry
• First-principles molecular quantum electrodynamics theory at all coupling strengths
• Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems
• Light-Matter Hybridization and Entanglement from the First-Principles
• Deep quantum Monte Carlo approach for polaritonic chemistry
• Auxiliary Field Quantum Monte Carlo for Electron-Photon Correlation