Machine Learning Force Fields (MLFF) should be accurate, efficient, and applicable to molecules, materials, and interfaces thereof. The first step toward ensuring broad applicability and reliability of MLFFs requires a robust conceptual understanding of how to map interacting electrons to interacting "atoms". Here I discuss two aspects: (1) how electronic interactions are mapped to atoms with a critique of the "electronic nearsightedness" principle, and (2) our developments of symmetry-adapted gradient-domain machine learning (sGDML) framework for MLFFs generally applicable for modeling of molecules, materials, and their interfaces. I highlight the key importance of bridging fundamental physical priors and conservation laws with the flexibility of non-linear ML regressors to achieve the challenging goal of constructing chemically-accurate force fields for a broad set of systems. Applications of sGDML will be presented for small and large (bio/DNA) molecules, pristine and realistic solids, and interfaces between molecules and 2D materials. [Refs] Sci. Adv. 3, e1603015 (2017); Nat. Commun. 9, 3887 (2018); Comp. Phys. Comm. 240, 38 (2019); J. Chem. Phys. 150, 114102 (2019); Sci. Adv. 5, eaax0024 (2019).
Electronic spectra of molecular systems represent critical data in many areas of science. However, their quantitative modelling is computationally demanding. In my talk, I will discuss several routes how these simulations can be accelerated and made more reliable. I proposed several statistical and data-based approaches increasing the efficiency and accuracy of electronic spectra simulations within the so-called nuclear ensemble model. However, their broader applicability will be discussed as well. The presented approaches are based on the correlation either between different electronic structure methods or among nuclear configurations representing the density of the initial state. For instance, a method of representative sampling is proposed, where a fast exploratory method is used to select a small subset of geometries representing the nuclear density. I will also discuss the application of machine learning techniques to the prediction of excited-state properties. The main problem stems from state crossings, which make the regression inefficient. I tackle this problem by reordering the states in several ways, resulting in increased accuracy of the applied machine learning algorithms. Finally, a statistically sound theory is used to optimise the signal-to-noise ratio of the estimated spectra and to quantify random errors. The concept of error in quantum chemistry, often underestimated in the community, will be discussed. I will show that error estimation can be crucial for a proper interpretation of the modelled data.
I will talk about the monitored Brownian Sachdev-Ye-Kitaev (SYK) model without and with errors [PRL 127 140601 and arXiv:2106.09635]. Without errors, the model exhibits a measurement-induced phase transition that can be understood as a symmetry-breaking transition of an effective Z4 magnet in the replica space. The errors describe the loss of information about the measurement outcomes and, when present, can be mapped to an emergent magnetic field in the Z4 magnet. I will discuss two cases: when errors are applied during the non-unitary evolution, the symmetry is explicitly broken independent of the measurement rate, leading to a volume-law Renyi entropy. When errors are applied at the end of the evolution, the error-induced magnetic field only exists near the boundary of the magnet and can lead to a pinning transition of domain walls, corresponding to error threshold of the quantum code prepared by the non-unitary SYK dynamics.
Fermions are often considered as somewhat strange quantum objects due to their anti-commuting properties. Cellular automata describe deterministic changes for bit-configurations, as for classical computing. At first sight these two issues do not seem to be much related. We show that probabilistic cellular automata, for which initial conditions are given by a probability distribution, can describe certain quantum many body systems of interacting fermions. The notions of wave functions, non-commuting operators for observables and quantum rules for expectation values arise in a natural way from the classical statistics for the probabilistic cellular automata. This constitutes an example how quantum mechanics can emerge from a classical statistical system. The famous particle-wave duality combines the discreteness of the bit observables or fermionic occupation numbers with the continuity of the probabilistic information and its evolution in time.