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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantum simulations employing connected moments expansions

Further advancement of quantum computing (QC) is contingent on enabling many-body models that avoid deep circuits and excessive use of CNOT gates. To this end, we develop a QC approach employing finite-order connected moment expansions (CMX) and affordable procedures for initial state preparation. We demonstrate the performance of our approach employing several quantum variants of CMX through the classical emulations on the H2 molecule potential energy surface and the Anderson model with a broad range of correlation strength. The results show that our approach is robust and flexible. Good agreements with exact solutions can be maintained even at the dissociation and strong correlation limits.

quantum computing, quantum chemistry, Electron cor↗
DOE OSTI2021

Dimensionality reduction of the many-body problem using coupled-cluster subsystem flow equations: classical and quantum computing perspective

We discuss reduced-scaling strategies employing recently introduced sub-system embedding sub-algebras coupled-cluster formalism (SES-CC) to describe many-body systems. These strategies utilize properties of the SES-CC formulations where the equations describing certain classes of sub- systems can be integrated into a computational flows composed coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be defined at the level of the CC Ansatz defined by selected classes of cluster amplitudes, which define the wave function ”memory” of possible partitionings of the many-body system into constituent sub-systems. One of the possible ways of solving these coupled problems is through implementing procedures, where the information is passed between the sub-systems in a self-consistent manner. As a special case, we consider local flow formulations where the so-called local character of correlation effects can be closely related to properties of sub-system embedding sub-algebras employing localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing double exponential unitary CC Ansatz (DUCC), where reduced dimensionality of constituent sub-problems offer a possibility of efficient utilization of limited quantum resources in modeling realistic systems.

Electron correlation, quantum chemistry, quantum c↗
DOE OSTI2023

Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select (U) scheme uses O(n) Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n 3 , a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: From Model Systems to Realistic Applications

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. Here, by extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Algorithms↗
DOE OSTI2026

Toward the “platinum standard” of quantum chemistry on quantum computers: Perturbative quadruple corrections in unitary coupled cluster theory

We propose a non-iterative, post-hoc correction to the unitary coupled cluster theory with the single, double, and triple excitations (UCCSDT) Ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this correction, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be truncated to sixth-order in many-body perturbation theory. Furthermore, a comparison between the UCC-based [Q-6] correction proposed in this work and analogous, “platinum standard” quadruple corrections proposed in conventional coupled cluster theory recognizes that [Q-6] is distinct from prior corrections since it is constructed entirely from internally connected components. Although trotterized (t) and full operator variants of UCCSDT exhibit errors in scans of small molecule potential energy surfaces that routinely exceed 1.6 mH, we find that t/UCCSDT[Q-6] is, nevertheless, able to achieve chemical accuracy as measured by the mean unsigned error.

Correlation energy↗
DOE OSTI2026

Stochastic tensor contraction for quantum chemistry

Many computational methods in ab initio quantum chemistry are formulated in terms of high-order tensor contractions, whose cost determines the size of system that can be studied. We introduce stochastic tensor contraction to perform such operations with greatly reduced cost, and present its application to the gold-standard quantum chemistry method, coupled cluster theory with up to perturbative triples. For total energy errors more stringent than chemical accuracy, we reduce the computational scaling to that of mean-field theory, while starting to approach the mean-field absolute cost, thereby challenging the existing cost-to-accuracy landscape. Benchmarks against state-of-the-art local correlation approximations further show that we achieve an order-of-magnitude improvement in both total computation time and error, with significantly reduced sensitivity to system dimensionality and electron delocalization. We conclude that stochastic tensor contraction is a powerful computational primitive to accelerate a wide range of quantum chemistry.

Chemical Physics (physics.chem-ph)↗
DOE OSTI2020

Toward DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: Electrons moving at relativistic speeds, close lying states, and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules in which all the three effects are present. These are the heavier transition metal compounds, lanthanides, and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and the density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs as we demonstrate on the system of TlH, AsH, and SbH.

Brandejs, Jan (ORCID:0000000221073095)↗
DOE OSTI2023

Non-perturbative many-body treatment of molecular magnets

Molecular magnets have received significant attention because of their potential applications in quantum information and quantum computing. A delicate balance of electron correlation, spin–orbit coupling (SOC), ligand field splitting, and other effects produces a persistent magnetic moment within each molecular magnet unit. The discovery and design of molecular magnets with improved functionalities would be greatly aided by accurate computations. However, the competition among the different effects poses a challenge for theoretical treatments. Electron correlation plays a central role since d- or f-element ions, which provide the magnetic states in molecular magnets, often require explicit many-body treatments. SOC, which expands the dimensionality of the Hilbert space, can also lead to non-perturbative effects in the presence of strong interaction. Furthermore, molecular magnets are large, with tens of atoms in even the smallest systems. We show how an ab initio treatment of molecular magnets can be achieved with auxiliary-field quantum Monte Carlo, in which electron correlation, SOC, and material specificity are included accurately and on an equal footing. Furthermore, the approach is demonstrated by an application to compute the zero-field splitting of a locally linear Co 2+ complex.

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

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction

Least Squares Tensor Hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wavefunc- tion based methods in quantum chemistry. However, previous work has demonstrated that the LS-THC factorization performs disproportionately worse in the description of wavefunction components (e.g. cluster amplitudes T 2 ) than Hamiltonian compo- nents (e.g. electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T 2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T 2 that is remarkably consistent across ten molecular species, three correlated wavefunctions, and four basis sets. This correlation feature portends the existence of a “pair-point kernel” missing in the usual LS-THC representation of the wavefunction, which critically depends upon pairs of grid points situated close to atoms and with inter-pair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Nuclear Fuel and Pu Redox Studies from The Glenn T. Seaborg Institute at Idaho National Laboratory

The Glenn T. Seaborg Institute at Idaho National Laboratory (INL-GTSI) focuses on advancing fundamental research in the actinide sciences by providing unique opportunities to early career scientists and engineers to gain experience studying the actinide elements and their associated systems. The INL-GTSI is built from three focus areas that are based on the expertise and supporting infrastructure at INL and include solid state chemistry and physics, solution phase chemistry and physics, and forensic and isotope science. INL is the lead Laboratory for nuclear energy research and development in the U. S. and the research on nuclear fuels performed under the INL-GTSI gives good examples of solid state studies. Uranium-Molybdenum (U-Mo) alloys are leading fuel candidates for conversion of high performance research and test reactors to low-enriched fuels. During irradiation, generated fission gas accumulates into bubbles and self-organizes into a gas bubble superlattice (GBS) that effectively stores fission gases and inhibits fuel swelling. A study on the early self- organizing behavior of the GBS shows that not only grain boundaries but the interfaces between the U-Mo matrix and uranium carbide (UC) impurities are important to GBS formation.[1] In solution, understanding the complex redox behavior of plutonium in aqueous environments is critical for establishing optimized nuclear waste reprocessing solvent systems and storage tank environments. INL-GTSI researchers have produced an experimentally validated multi-scale model of the gamma radiation induced behavior of plutonium ions in concentrated aqueous HNO3 solutions.[2] Here, gamma radiation effected only minimal steady state changes in the redox distribution of the plutonium oxidation states. The redox cycling between Pu(IV) and Pu(III) is demonstrated to be mediated by the •OH/NO3• radical oxidation of Pu(III) and the H2O2/HNO3 driven reduction of Pu(IV). The INL-GTSI offers young researchers the unique chance to work directly with actinide bearing materials in a U. S. National Laboratory environment. Further topical areas of interest to the INL-GTSI include, but are not limited to, fundamental actinide properties, structure/property (electronic, magnetic, thermal) relations, actinide quantum criticality, f- electron interactions, electron correlations, computational studies, new phases, defect effects, interface interactions, isotope production and separation, forensic analytical chemistry, structure and dynamic properties of actinides in non-aqueous media, separations chemistry and kinetics for advanced nuclear fuel cycles, radiation effects, and innovative and advanced ligand design for complexation of the actinides.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

A new “gold standard”: Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the “gold standard” CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Methane Adsorption on Heteroatom-Modified Maquettes of Porous Carbon Surfaces

Experimental and theoretical studies disagree on the energetics of methane adsorption on carbon materials. However, this information is critical for the rational design and optimization of the structure and composition of adsorbents for natural gas storage. The delicate nature of dispersion interactions, polarization of both the adsorbent and the adsorbate, interplay between H-bonding and tetrel bonding, and induced dipole/Coulomb interactions inherent to methane physisorption require computational treatment at the highest possible level of theory. In this study, we employed the smallest reasonable computational model, a maquette of porous carbon surfaces with a central site for substitution and methane binding. The most accurate predictions of methane adsorption energetics were achieved by electron-correlated molecular orbital theory CCSD(T) and hybrid density functional theory MN15 calculations employing a saturated, all-electron basis set. Here, the characteristic geometry of methane adsorption on a carbon surface (“lander approach”) arises due to bonding interactions of the adsorbent π-system with the proximal H–C bonds of methane, in addition to tetrel bonding between the antibonding orbital of the distal C–H bond and the central atom of the maquette (C, B, or N). The polarization of the electron density, structural deformations, and the comprehensive energetic analysis clearly indicate a ∼3 kJ mol –1 preference for methane binding on the N-substituted maquette. The B-substituted maquette showed a comparable or lower binding energy than the unsubstituted, pure C model, depending on the level of theory employed. The calculated thermodynamic results indicate a strategy for incorporating electron-enriched substitutions (e.g., N) into carbon materials as a way to increase methane storage capacity over electron-deficient (e.g., B) modifications. The thermochemical analysis was revised for establishing a conceptual agreement between the experimental isosteric heat of adsorption and the binding enthalpies from statistical thermodynamics principles.

03 NATURAL GAS↗
DOE OSTI2020

Correlation matrix renormalization theory in multi-band lattice systems

An appropriate treatment of electronic correlation effects plays an important role in accurate descriptions of physical and chemical properties of real materials. The recently proposed correlation matrix renormalization theory with sum rule correction (CMR) for studying correlated-electron materials has shown good performance in molecular systems and a periodic hydrogen chain in comparison with various quantum chemistry and quantum Monte Carlo calculations. Additionally, this work gives a detailed formulation and computational code implementation of CMR in multi-band periodic lattice systems. This lattice CMR ab initio theory is highly efficient, has no material specific adjustable parameters, and has no double counting issues faced by the hybrid approaches like LDA + U, DFT + DMFT and DFT + GA type theories. Benchmark studies on materials with s and p orbitals in this study show that CMR in its current implementation consistently performs well for these systems as the electron correlation increases from the bonding region to the bond breaking region.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

The Singlet–Triplet Gap of Cyclobutadiene: The CIPSI-Driven CC( P ; Q ) Study

An accurate determination of singlet−triplet gaps in biradicals, including cyclobutadiene in the automerization barrier region where one has to balance the substantial nondynamical many-electron correlation effects characterizing the singlet ground state with the predominantly dynamical correlations of the lowest-energy triplet, remains a challenge for many quantum chemistry methods. High-level coupled-cluster (CC) approaches, such as the CC method with a full treatment of singly, doubly, and triply excited clusters (CCSDT), are often capable of providing reliable results, but routine application of such methods is hindered by their high computational costs. We have recently proposed a practical alternative to converging the CCSDT energetics at small fractions of the computational effort, even when electron correlations become stronger and connected triply excited clusters are larger and nonperturbative, by merging the CC(P;Q) moment expansions with the selected configuration interaction methodology abbreviated as CIPSI. We demonstrate that one can accurately approximate the highly accurate CCSDT potential surfaces characterizing the lowest singlet and triplet states of cyclobutadiene along the automerization coordinate and the gap between them using tiny fractions of triply excited cluster amplitudes identified with the help of relatively inexpensive CIPSI Hamiltonian diagonalizations.

Basis sets↗
DOE OSTI2022

Simulating Effective QED on Quantum Computers

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T -gates needed to perform such simulations on a 3 D lattice of n s sites scales at worst as O ( n s 3 / ϵ ) 1 + o ( 1 ) in the thermodynamic limit for position basis simulations and O ( n s 4 + 2 / 3 / ϵ ) 1 + o ( 1 ) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O ~ ( n s 2 + 2 / 3 / ϵ ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O ~ ( n s 5 + 2 / 3 / ϵ ) . We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 10 13 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2023

Sub-system self-consistency in coupled cluster theory

Here, in this article, we provide numerical evidence indicating that the single-reference coupled-cluster (CC) energies can be calculated alternatively to their copybook definition. We demonstrate that the CC energy can be reconstructed by diagonalizing the effective Hamiltonians describing correlated sub-systems of the many-body system. In the extreme case, we provide numerical evidence that the CC energy can be reproduced through the diagonalization of the effective Hamiltonian describing sub-system composed of a single electron. These properties of the CC formalism can be exploited to design protocols to define effective interactions in sub-systems used as probes to calculate the energy of the entire system and introduce a new type of self-consistency for approximate CC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Frontiers in divalent $f$-block chemistry

Divalent f-block chemistry has undergone rapid expansion in recent years, driven by advances in the stabilization of low-valent lanthanide and actinide complexes. Although f-elements were historically accessed in the +3 or higher oxidation states, the isolation of +2 species has revealed unusual spectroscopic signatures, distinct bonding motifs, and multiple accessible electronic configurations that influence their chemical and physical properties. These developments have generated opportunities in areas including quantum information science, molecular magnetism, catalysis, and luminescence. Computational chemistry has played a pivotal role in interpreting the electronic structure and reactivity of these systems. However, accurately modeling divalent f-block complexes remains challenging because of strong electronic correlation, multiconfigurational character, and the presence of close-in-energy competing electronic states. As experimental capabilities and theoretical methodologies continue to advance, a comprehensive assessment of divalent chemistry is both timely and needed. In this Review, we integrate experimental and theoretical perspectives to provide a systematic analysis of divalent lanthanide and actinide complexes across the f-block series. We critically assess the role of ligands in determining competing ground-state configurations (f n d 1 vs. f n+1 ) resulting in their distinct spectroscopic, magnetic, and bonding properties. Finally, we discuss emerging strategies for predictive modeling and rational design of low-valent f-block molecular systems, with potential applications ranging from dinitrogen reduction to quantum technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗