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We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…

In condensed matter physics, particularly in perovskite materials, the rotational motion of molecules and ions is associated with important issues such as ion conduction mechanism. Constrained Molecular Dynamics (MD) simulations offer a…

Chemical Physics · Physics 2024-08-05 Jitai Yang , Ke Li , Jia Liu , Jia Nie , Hui Li

Machine Learning (ML) models are trained using historical data to classify new, unseen data. However, traditional computing resources often struggle to handle the immense amount of data, commonly known as Big Data, within a reasonable time…

Quantum Physics · Physics 2024-11-01 Minati Rath , Hema Date

We explore the application of computer vision and machine learning (ML) techniques to predict material properties (e.g. compressive strength) based on SEM images. We show that it's possible to train ML models to predict materials…

This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model. We have developed a more concise formula for calculating the cluster's…

Quantum Physics · Physics 2025-12-24 Hengyue Li , Yusheng Yang , Pin Lv , Jinglong Qu , Zhe-Hui Wang , Jian Sun , Shenggang Ying

The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…

Strongly Correlated Electrons · Physics 2007-05-23 P. Ziesche , F. Tasnadi

CP2K is a versatile open-source software package for simulations across a wide range of atomistic systems, from isolated molecules in the gas phase to low-dimensional functional materials and interfaces, as well as highly symmetric…

The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates, based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the…

Nuclear Theory · Physics 2020-12-22 Takayuki Myo , Kiyoshi Kato

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first principles based virtual sampling of this space, for example…

Chemical Physics · Physics 2021-06-23 Bing Huang , O. Anatole von Lilienfeld

Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum statistics of vibrations…

Materials Science · Physics 2011-05-30 Jean-Louis Barrat , David Rodney

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

Quantum Physics · Physics 2022-05-18 Alexis Ralli , Michael I. Williams , Peter V. Coveney

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this Review, we provide a structured overview of recent advances that bridge foundational…

Quantum Physics · Physics 2026-02-25 Vinit Singh , Amandeep Singh Bhatia , Mandeep Kaur Saggi , Manas Sajjan , Sabre Kais

High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…

Quantum Physics · Physics 2019-10-29 Alain Tchagang , Julio Valdés

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental…

Computational Physics · Physics 2021-04-14 Stefan Chmiela , Huziel E. Sauceda , Alexandre Tkatchenko , Klaus-Robert Müller

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large…

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…

Mesoscale and Nanoscale Physics · Physics 2016-10-14 Mariana M. Odashima , Beatriz G. Prado , E. Vernek

Quantum Mechanics/Molecular Mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and…

Chemical Physics · Physics 2020-10-29 Jorge Nochebuena , Sehr Naseem-Khan , G. Andrés Cisneros

The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…

Condensed Matter · Physics 2007-05-23 Karen Hallberg

In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…

Materials Science · Physics 2020-04-15 Igor Ying Zhang , Andreas Grüneis

Quantum computing (QC) and machine learning (ML), taken individually or combined into quantum-assisted ML (QML), are ascending computing paradigms whose calculations come with huge potential for speedup, increase in precision, and resource…