We train a neural network as the universal exchange–correlation functional of density-functional theory that simultaneously reproduces both the exact exchange–correlation energy and the potential. ...This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn–Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange–correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task in quantum science. While several algorithms have been ...designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative schemes. Most recently, deep neural networks have been used for quantum dynamics, but current architectures are highly dependent on the physics of the particular system and usually limited to population dynamics. Here we introduce an artificial-intelligence-based surrogate model that solves dissipative quantum dynamics by parametrizing quantum propagators as Fourier neural operators, which we train using both data set and physics-informed loss functions. Compared with conventional algorithms, our quantum neural propagator avoids time-consuming iterations and provides a universal superoperator that can be used to evolve any initial quantum state for arbitrarily long times. To illustrate the wide applicability of the approach, we employ our quantum neural propagator to compute the population dynamics and time-correlation functions of the Fenna–Matthews–Olson complex.
Abstract Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state ...quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix γ as a variable but ...still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals Fγ for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates with N_{BEC}≈N condensed bosons, the respective gradient forces are found to diverge, ∇_{γ}F∝1/sqrt1-N_{BEC}/N, providing a comprehensive explanation for the absence of complete condensation in nature.
Abstract
The homogeneous electron liquid is a cornerstone in quantum physics and chemistry. It is an archetypal system in the regime of slowly varying densities in which the exchange-correlation ...energy can be estimated with many methods. For high densities, the behavior of the ground-state energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions and compute its correlation energy beyond the random phase approximation (RPA). We employ the approach developed by Singwi, Tosi, Land, and Sjölander (STLS), whose description of the electronic density response for 2
D
and 3
D
for metallic densities is known to be comparable to Quantum Monte-Carlo. For higher dimensions, we compare the results obtained for the correlation energy with the values previously obtained using RPA. We find that in agreement with what is known for 2 and 3 dimensions, the RPA tends to over-correlate the liquid also at higher dimensions. We furthermore provide new analytical formulae for the unconventional-dimensional case both for the real and imaginary parts of the Lindhard polarizability and for the local field correction of the STLS theory, and illustrate the importance of the plasmon contribution at those high dimensions.
The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighborhood of active orbitals around the Fermi level. The respective ...wavefunction ansatzes which involve all possible electron configurations of active orbitals can be characterized by the saturation of a certain number of Pauli constraints 0 ≤ n i ≤ 1 , identifying the occupied core orbitals (ni = 1) and the inactive virtual orbitals (nj = 0). In Part I, we generalize this crucial concept of active spaces by referring to the generalized Pauli constraints. To be more specific, we explain and illustrate that the saturation of any such constraint on fermionic occupation numbers characterizes a distinctive set of active electron configurations. A converse form of this selection rule establishes the basis for corresponding multiconfigurational wavefunction ansatzes. In Part II, we provide rigorous derivations of those findings. Moroever, we extend our results to non-fermionic multipartite quantum systems, revealing that extremal single-body information has always strong implications for the multipartite quantum state. In that sense, our work also confirms that pinned quantum systems define new physical entities and the presence of pinnings reflect the existence of (possibly hidden) ground state symmetries.
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent ...progress in the
N
-representability problem of the one-body density matrix for pure states, we propose a method to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.
Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the
N
-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation.
We develop an orbital-free functional framework to compute one-body quasiprobabilities for both fermionic and bosonic systems. Since the key variable is a quasidensity, this theory circumvents the ...problems of finding the Pauli potential or approximating the kinetic energy that are known to limit the applicability of standard orbital-free density functional theory. We present a set of strategies to (a) compute the one-body Wigner quasiprobability in an orbital-free manner from the knowledge of the universal functional and (b) obtain those functionals from the functionals of the one-body reduced density matrix (1-RDM). We find that the universal functional of optical lattices results from a translation, a contraction, and a rotation of the corresponding functional of the 1-RDM, revealing the strong connection between these two functional theories. Furthermore, we relate the key concepts of Wigner negativity and v representability.
Abstract
Fermionic natural occupation numbers do not only obey Pauli's exclusion principle but are
even stronger restricted by so-called generalized Pauli constraints. Whenever given natural
...occupation numbers lie on the boundary of the allowed region the corresponding
N
-fermion
quantum state has a significantly simpler structure. We recall the recently proposed
natural extension of the Hartree–Fock ansatz based on this structural simplification. This
variational ansatz is tested for the lithium atom. Intriguingly, the underlying mathematical
structure yields universal geometrical bounds on the correlation energy reconstructed by
this ansatz.
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