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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗
DOE OSTI2022

Coupled Cluster Downfolding Theory: towards universal many-body algorithms for dimensionality reduction of composite quantum systems in chemistry and materials science

Abstract The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems commonly encountered in materials science and chemistry. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.

Bauman, Nicholas P.↗
DOE OSTI2026

Theory of ab initio downfolding with arbitrary-range electron-phonon coupling

Ab initio downfolding describes the electronic structure of materials within a low-energy subspace, often around the Fermi level. Typically starting from mean-field calculations, this framework allows for the calculation of one- and two-electron interactions, and the parametrization of a many-body Hamiltonian representing the active space of interest. The subsequent solution of such Hamiltonians can provide insights into the physics of strongly correlated materials. While phonons can substantially screen electron-electron interactions, electron-phonon coupling has been commonly ignored within ab initio downfolding, and when considered, this is done only for short-range coupling. Here we propose a theory of ab initio downfolding that accounts for short- and long-range electron-phonon coupling on equal footing. Our practical computational implementation is readily compatible with current downfolding approaches. We apply our approach to polar materials MgO and GeTe, and we reveal the importance of both short-range and long-range electron-phonon coupling in determining the magnitude of electron-electron interactions. Our results show that in the static limit, phonons reduce the on-site repulsion between electrons by 40% for MgO and by 79% for GeTe. Our framework also predicts that overall attractive nearest-neighbor interactions arise between electrons in GeTe, consistent with superconductivity in this material.

Tubman, Norm M↗
DOE OSTI2025

Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers

The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca 2 Cu O 3 , the excitonic ground state of monolayer W Te 2 , and the charge-ordered state of correlated metal Sr VO 3 . Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.

Alvertis, Antonios M. [NASA, Ames; LBNL, Berkeley]↗
NASA NTRSDate not supplied

Downfolding Complex Materials Problems Onto Model Hamiltonians for Quantum Computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios Markos Alvertis↗
NASA NTRSDate not supplied

Downfolding complex materials problems onto model Hamiltonians for quantum computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios M. Alvertis↗
DOE OSTI2024

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H 2 , Methylene, Formaldehyde, and Nitroxyl.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

The accuracies of effective interactions in downfolding coupled-cluster approaches for small-dimensionality active spaces

Here, this paper evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Renormalization of states and quasiparticles in many-body downfolding

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We show that the renormalization factor provides a unique measure of the quality of the compression as it directly represents the projection between the approximate stationary state of the many-body Hamiltonian and the full many-body wavefunction. Hence, the renormalization factor is a measure of fidelity between the effective (reduced-rank) description and the full many-body treatment for arbitrary (i.e., ground and excited) states. When the entire problem is mapped on a system of interacting quasiparticles [Romanova et al., npj Comput. Mater. 9, 126 (2023)], the effective Hamiltonians can faithfully reproduce the physics only when a clear energy scale separation exists between the subsystems and their environment. We also demonstrate that it is necessary to include quasiparticle renormalization at distinct energy scales, capturing the distinct interaction between subsystems and their surrounding environments. Numerical results from simple, exactly solvable models highlight the limitations and strengths of this approach, particularly for ground and low-lying excited states. This work lays the groundwork for applying dynamical downfolding techniques to problems concerned with (quantum) interfaces.

Green-functions technique↗
DOE OSTI2025

Qubit-Efficient Quantum Chemistry with the ADAPT Variational Quantum Eigensolver and Double Unitary Downfolding

Here, in this work, we combine the recently developed double unitary coupled cluster (DUCC) theory with the adaptive, problem-tailored variational quantum eigensolver (ADAPT-VQE) to explore the accuracy of unitary downfolded Hamiltonians for quantum simulation of chemistry. We benchmark the ability of DUCC effective Hamiltonians to recover dynamical correlation energy outside of an active space. We consider the effects of strong correlation, commutator truncation, higher-body terms, and approximate external amplitudes on the accuracy of these effective Hamiltonians. When combining these DUCC Hamiltonians with ADAPT-VQE, we observe similar convergence of the ground state as compared with bare active space Hamiltonians, demonstrating that DUCC Hamiltonians provide increased accuracy without increasing the load on the quantum processor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Dynamical downfolding for localized quantum states

We introduce an approach to treat localized correlated electronic states in the otherwise weakly correlated host medium. Here, the environment is dynamically downfolded on the correlated subspace. It is captured via renormalization of one and two quasiparticle interaction terms which are evaluated using many-body perturbation theory. We outline the strategy on how to take the dynamical effects into account by going beyond the static limit approximation. Further, we introduce an efficient stochastic implementation that enables treating the host environment with a large number of electrons at a minimal computational cost. For a small explicitly correlated subspace, the dynamical effects are critical. We demonstrate the methodology by reproducing optical excitations in the negatively charged NV center defect in diamond, that agree with experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Ab initio ground states of strongly-correlated materials on quantum computers

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We benchmark the solution of Hubbard-like models obtained through downfolding by utilizing a classical tensor network implementation of variational quantum eigensolvers (VQE), and we reveal a strategy for driving the optimization through a hybrid minimization of the energy and maximization of the overlap with an approximate solution obtained through low-cost computational methods. This results in a reduction of the energy error by orders of magnitude compared to conventional VQE approaches, and allows us to reproduce long-range correlations for the first time. We demonstrate our first-principles approach for diverse strongly-correlated materials, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca 2 CuO 3 , the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO 3 . Our efficient computational implementation allows us to simulate large systems with up to 54 qubits and encompassing up to four correlated bands, which is indicative of the complexity that our framework can address.

Antonios M Alvertis↗
DOE OSTI2023

Enabling Scalable VQE Simulation on Leading HPC Systems

Large-scale simulations of quantum circuits pose significant challenges, especially in the context of quantum chemistry, due to the number of qubits, circuit depth, and the number of circuits needed per problem. High-performance computing (HPC) systems offer massive computational capabilities that could help overcome these obstacles. We developed a high-performance quantum circuit simulator, called NWQ-Sim, and demonstrate its capability to simulate large quantum chemistry problems on NERSC's Perlmutter supercomputer. Integrating NWQ-Sim with XACC, we have executed QPE and VQE algorithms for downfolded quantum chemistry systems at unprecedented scales. Our work demonstrates the potential of leveraging HPC resources to advance quantum chemistry and other applications of near-term quantum devices.

Wang, Meng↗
NASA NTRS1977

Cratering motions and structural deformation in the rim of the Prairie Flat multiring explosion crater

Cratering motions and structural deformation are described for the rim of the Prairie Flat multiring crater, 85.5 m across and 5.3 m deep, which was formed by the detonation of a 500-ton TNT surface-tangent sphere. The terminal displacement and motion data are derived from marker cans and velocity gages emplaced in drill holes in a three-dimensional matrix radial to the crater. The integration of this data with a detailed geologic cross section, mapped from deep trench excavations through the rim, provides a composite view of the general sequence of motions that formed a transiently uplifted rim, overturned flap, inverted stratigraphy, downfolded rim, and deformed strata in the crater walls. Preliminary comparisons with laboratory experimental cratering and with numerical simulations indicate that explosion craters of the Prairie Flat-type generated by surface and near-surface energy sources tend to follow predictable motion sequences and produce comparable structural deformation. More specifically, central uplift and multiring impact craters with morphologies and structures comparable to Prairie Flat are inferred to have experienced similar deformational histories of the rim, such as uplift, overturning, terracing, and downfolding.

Roddy, D. J.↗