As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to ...execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.
We introduce density matrix embedding theory (DMET), a quantum embedding theory for computing frequency-independent quantities, such as ground-state properties, of infinite systems. Like dynamical ...mean-field theory, DMET maps the bulk interacting system to a simpler impurity model and is exact in the noninteracting and atomic limits. Unlike dynamical mean-field theory, DMET is formulated in terms of the frequency-independent local density matrix, rather than the local Green's function. In addition, it features a finite, algebraically constructible bath of only one bath site per impurity site, with no bath discretization error. Frequency independence and the minimal bath make DMET a computationally simple and efficient method. We test the theory in the one-dimensional and two-dimensional Hubbard models at and away from half filling, and we find that compared to benchmark data, total energies, correlation functions, and metal-insulator transitions are well reproduced, at a tiny computational cost.
The electronic structure of the nitrogenase metal cofactors is central to nitrogen fixation. However, the P-cluster and FeMo cofactor, each containing eight Fe atoms, have eluded detailed ...characterization of their electronic properties. We report on the low-energy electronic states of the P-cluster in three oxidation states through exhaustive many-electron wavefunction simulations enabled by new theoretical methods. The energy scales of orbital and spin excitations overlap, yielding a dense spectrum with features that we trace to the underlying atomic states and recouplings. The clusters exist in superpositions of spin configurations with non-classical spin correlations, complicating interpretation of magnetic spectroscopies, whereas the charges are mostly localized from reorganization of the cluster and its surroundings. On oxidation, the opening of the P-cluster substantially increases the density of states, which is intriguing given its proposed role in electron transfer. These results demonstrate that many-electron simulations stand to provide new insights into the electronic structure of the nitrogenase cofactors.
PySCF: the Python‐based simulations of chemistry framework Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S. ...
Wiley interdisciplinary reviews. Computational molecular science,
January/February 2018, Letnik:
8, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Python‐based simulations of chemistry framework (PySCF) is a general‐purpose electronic structure platform designed from the ground up to emphasize code simplicity, so as to facilitate new method ...development and enable flexible computational workflows. The package provides a wide range of tools to support simulations of finite‐size systems, extended systems with periodic boundary conditions, low‐dimensional periodic systems, and custom Hamiltonians, using mean‐field and post‐mean‐field methods with standard Gaussian basis functions. To ensure ease of extensibility, PySCF uses the Python language to implement almost all of its features, while computationally critical paths are implemented with heavily optimized C routines. Using this combined Python/C implementation, the package is as efficient as the best existing C or Fortran‐based quantum chemistry programs. In this paper, we document the capabilities and design philosophy of the current version of the PySCF package. WIREs Comput Mol Sci 2018, 8:e1340. doi: 10.1002/wcms.1340
This article is categorized under:
Structure and Mechanism > Computational Materials Science
Electronic Structure Theory > Ab Initio Electronic Structure Methods
Software > Quantum Chemistry
The PySCF package provides a Python programming environment to study the electronic structure of molecules and solids.
We extend our density matrix embedding theory (DMET) Phys. Rev. Lett. 2012, 109, 186404 from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary ...fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating complex strongly coupled, strongly correlated systems in terms of their individual fragments.
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