Aspuru-Guzik, A.

Pérez Paz, A.

Rubio, A.

Sanders, J.

English

MPG.PuRe

Undersample Bmatrices Recover A via compressed sensing  Application of Compressed Sensing to Quantum  Chemistry  Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA.Nano-Bio Spectroscopy Group, University of the Basque Country UPV/EHU, San Sebastián, Spain.Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany.   •  .  • (B) Recovering a Matrix with Compressed Sensing (C) Compressed Sensing for Sparse Matrices (F) (14,0) carbon nanotube: tight-binding  • •    (D) Approach for Electronic Structure Calculations Compressed sensing for mul/ dimensional spectroscopy  Compressed Sensing recovers sparse  matrices regardless where non-zeros are.      (A) Research Objective: Use compressed sensing to calculate quantum chemistry matrices (Hamiltonian, Fockian, etc) cheaply without having to compute each matrix element.Publications: • X. Andrade, J. N. Sanders, & A. Aspuru‐Guzik. Application of compressed sensing to the simulation of atomic systems. PNAS 109, 35 (2012). arXiv: 1205.6485.• J. N. Sanders, X. Andrade, & A. Aspuru‐Guzik. Compressed Sensing for the Fast Computation of Matrices: Application to Mol cular Vibrations. ACS Cent. Sci. 1 (1) 24-32 (2015).Acknowledgments:A.P.P. thanks the support from "Ayuda para la Especialización de Personal Investigador del Vicerrectorado de Investigación UPV/EHU-2013" & Duncan J. Mowbray for his help with Inkscape (H) Future Research Plan• Investigate electron-phonon coupling matrix elements.• Solving +Dyson Equation, Hubbard Hamiltonian?• Application to other matrix problems in physics/chemistry.(G) Application to hybrid PBE0/B3LYP FockiansWe accurately recover all matrix elements with as low as 40 % of undersampling. Example: cheaply approximate the eigenvectors.Step1: Cheaply locate a basisin which the matrix is sparse.Step 2: Cheaply recover this sparse matrix using compressed sensing.(E) The Kronig-Penney model Jacob N. Sanders, Alejandro Pérez Paz, Alán Aspuru-Guzik, Angel Rubio 56 C atoms/unit cell, diameter 1.1065 nm.DFTB+ code: PRB 58, 7260 (1998).AT-GC Watson-Crick stacked base pairsfrom JPCB 114, 1191-1203 (2010).Errors in a.u.Physica B 406, 4373-4380 (2011)Sparse randommatrix A to recoverApply Incoherent Change-of-Basis Matrix P(e.g. discrete cosine transform)A is a sparse matrix that can be recovered with our procedure. A=H(hybrid) in basis of cheap KS orbitalsH(hybrid) in PW/AO basiserrors in a.u.Errors in eVH(X) in PW/AO basis A=H(X) in basis of eigenvectors of H(G)

Application of Compressed Sensing to Quantum Chemistry

https://pure.mpg.de/pubman/item/item_2179750_1/component/file_2179748/poster_harnack.pdf

Application of Compressed Sensing to Quantum Chemistry

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