AA2 – Nano and Quantum Technologies



Deep Backflow for Accurate Solution of the Electronic Schrödinger Equation

Project Heads

Jan Hermann (until 10/2022), Jens Eisert, Frank Noé

Project Members

Zeno Schätzle

Project Duration

01.04.2021 − 31.03.2024

Located at

FU Berlin


Accurate and general solution of the electronic Schrödinger equation is one of the great challenges in computational materials science, since it provides straightforward access to many material properties. Among the numerous approximate methods, quantum Monte Carlo provides a platform for in-principle exact numerical solutions at favorable computational cost, but in practice is limited by the flexibility of the available wave function ansatzes. The cornerstone of this issue is a faithful representation of the so-called nodal surface, on which the antisymmetric electronic wave function changes sign. This project aims to establish a novel computational technique based on deep neural networks, called deep backflow, as a general solution to the nodal-surface representation problem. This will overcome the only existing fundamental limitation to the accuracy of quantum Monte Carlo calculations, opening the possibility of highly accurate electronic-structure calculations for much larger systems than previously possible.

Related Publications

  • J. Hermann, J. Spencer, K. Choo, A. Mezzacapo, W. M. C. Foulkes, D. Pfau, G. Carleo, and F. Noé, ‘Ab-initio quantum chemistry with neural-network wavefunctions’. Nat. Rev. Chem., vol. 7, no. 10, p. 692-709, Oct. 2023, doi: 10.1038/s41570-023-00516-8
  • Z. Schätzle, B. Szabó, M. Mezera, J. Hermann, and F. Noé, ‘DeepQMC: an open-source software suite for variational optimization of deep-learning molecular wave functions’. J. Chem. Phys., vol. 159, no. 9, p. 094108, Sep. 2023, doi: 10.1063/5.0157512
  • P. A. Erdman and F. Noé, ‘Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning’, PNAS Nexus, p. pgad248, Aug. 2023, doi: 10.1093/pnasnexus/pgad248.
  • T. Kirschbaum, B. von Seggern, J. Dzubiella, A. Bande, and F. Noé, ‘Machine Learning Frontier Orbital Energies of Nanodiamonds’, J. Chem. Theory Comput., vol. 19, no. 14, pp. 4461–4473, Jul. 2023, doi: 10.1021/acs.jctc.2c01275.
  • M. T. Entwistle, Z. Schätzle, P. A. Erdman, J. Hermann, and F. Noé, ‘Electronic excited states in deep variational Monte Carlo’, Nat Commun, vol. 14, no. 1, Art. no. 1, Jan. 2023, doi: 10.1038/s41467-022-35534-5.
  • P. A. Erdman, G. M. Andolina, V. Giovannetti, and F. Noé, ‘Reinforcement learning optimization of the charging of a Dicke quantum battery’. arXiv, Dec. 23, 2022. doi: 10.48550/arXiv.2212.12397.
  • S. M. Moosavi et al., ‘A data-science approach to predict the heat capacity of nanoporous materials’, Nat. Mater., vol. 21, no. 12, Art. no. 12, Dec. 2022, doi: 10.1038/s41563-022-01374-3.
  • F. Musil, I. Zaporozhets, F. Noé, C. Clementi, and V. Kapil, ‘Quantum dynamics using path integral coarse-graining’, The Journal of Chemical Physics, vol. 157, no. 18, p. 181102, Nov. 2022, doi: 10.1063/5.0120386.
  • P. Abiuso, P. A. Erdman, M. Ronen, F. Noé, G. Haack, and M. Perarnau-Llobet, ‘Optimal Thermometers with Spin Networks’. arXiv, May 16, 2023. doi: 10.48550/arXiv.2211.01934.
  • P. A. Erdman and F. Noé, ‘Driving black-box quantum thermal machines with optimal power/efficiency trade-offs using reinforcement learning’. arXiv, Apr. 10, 2022. doi: 10.48550/arXiv.2204.04785.
  • P. A. Erdman and F. Noé, ‘Identifying optimal cycles in quantum thermal machines with reinforcement-learning’, npj Quantum Inf, vol. 8, no. 1, Art. no. 1, Jan. 2022, doi: 10.1038/s41534-021-00512-0.
  • S. Klus, P. Gelß, F. Nüske, and F. Noé, ‘Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry’, Mach. Learn.: Sci. Technol., vol. 2, no. 4, p. 045016, Aug. 2021, doi: 10.1088/2632-2153/ac14ad.
  • Z. Schätzle, J. Hermann, and F. Noé, ‘Convergence to the fixed-node limit in deep variational Monte Carlo’, J. Chem. Phys., vol. 154, no. 12, p. 124108, Mar. 2021, doi: 10.1063/5.0032836.

Related Pictures

Cuts through the nodal surfaces of wavefunctions for the Lithium atom.
Cuts through the nodal surfaces of wavefunctions for the Lithium atom.