arXiv subjects

Vibin Abraham

Publications and source records attributed to Vibin Abraham.

17 recordsLinked to original sources

arXiv2026

Toward Resilient Many-Body Formulations under Incomplete Correlation Models: A Dual-Space Variational Formulation

Quantum simulations of correlated many-body systems will inevitably operate with imperfect information: the prepared states may arise from incomplete or approximate ansatze, while their measured Hamiltonian and overlap matrix elements are additionally affected by hardware and statistical noise. Robust quantum algorithms will be those that can improve upon reliable lower-level descriptions in spite of these imperfections. We introduce a dual-space nonorthogonal configuration-interaction (DS-NOCI) framework built around this principle. Rather than replacing a classically accessible NOCI reference manifold with correlated quantum states, DS-NOCI retains both spaces and couples them variationally. The reference sector provides a stable many-body backbone, while the quantum states contribute whatever additional correlation directions they contain. With exact matrix elements, the enlarged dual space gives a ground-state energy no higher than either the reference-only NOCI or correlated-only quantum-NOCI spaces, ensuring that an incomplete correlation model cannot degrade the underlying variational description. The additional reference--correlated matrix elements require only one correlated state preparation and are therefore less demanding than the correlated--correlated block already required by quantum variant of NOCI. Molecular benchmarks further show enhanced resilience to imperfect amplitudes and noisy matrix elements. DS-NOCI thus provides a general strategy for building quantum many-body formulations that remain useful when both correlation models and quantum computations are necessarily incomplete and noisy.

quant-ph↗

arXiv2026

Geometry-Dependent Nonlocal Valence Screening Following Core Ionization of the Water Dimer

Core ionization is spatially localized, but the correlated valence response that screens the resulting hole need not be. Using the water dimer as a minimal hydrogen-bonded system, we ask whether acceptor-site O~1s ionization recruits valence channels on the neighboring donor molecule and how proton displacement redistributes that response. We introduce correlated shifted-start real-time $\Lambda$-coupled-cluster theory to connect the core-hole spectrum with orbital- and fragment-resolved screening pathways. At equilibrium, the satellite response contains donor-local and intermolecular charge-transfer-like contributions. Their intermolecular origin is supported by the strong suppression of both contributions when the monomers are separated. In a fixed-nuclei geometry scan, elongating the hydrogen-bonded donor O--H bond nearly doubles their combined share of the satellite response, while analysis of the first approximately 10~fs of the fixed-nuclei electronic response reveals stronger modulation involving a donor-localized valence orbital. More broadly, this work shows how localized core ionization can serve as a site-selective probe of electronic communication, with satellite structure revealing how nuclear geometry redirects many-electron screening through molecular environments.

physics.chem-ph↗

arXiv2026

Unified Uncertainty Quantification Framework Bridging Noisy Quantum Backends Across Variational Quantum Algorithms and Quantum Signal Processing

We present an uncertainty quantification (UQ) framework for application level benchmarking and characterization of noisy quantum backends. The framework compares two workload classes under one statistical pipeline: noisy intermediate scale quantum (NISQ) variational quantum algorithms (VQAs) and Quantum Singular Value Transformation (QSVT) based Green's function reconstruction. For the VQA branch, we evaluate ten benchmark families spanning chemistry, optimization, simulation, compiling, linear solving, partial differential equations, metrology, error correction, tomography, and channel fidelity estimation. For the QSVT branch, we reconstruct orbital resolved Green's functions and spectral peaks from a block encoded real time propagator. The workflow combines Bayesian optimization, posterior distribution refinement, sensitivity analysis, robust parameter density estimation, backend ranking, noise correlation, and resource estimation analysis. Instead of reporting only one best parameter vector, the framework identifies robust parameter regions, residual gaps to ideal behavior, backend specific failure modes, and calibration sensitive uncertainty. The result is a common benchmark for variational and non-variational workloads that measures how reliably each backend reaches useful task level behavior.

cs.ET↗

arXiv2026

All-Electron Relativistic Fully Self-Consistent $GW$ Study of Heteronuclear Actinide-Containing Diatomics

The fully self-consistent $GW$ (sc$GW$) approximation provides a Green's-function approach that is starting-point independent and offers a favorable cost-to-accuracy balance compared to high-level wavefunction methods. Here, we present an all-electron sc$GW$ study of uranium-containing diatomics (UC, UN, UO, and UF), incorporating relativistic effects through the exact two-component (X2C) formalism. We evaluate adiabatic ionization energies as well as electron-attachment and detachment energetics (AEA and VDE), together with equilibrium structures and harmonic vibrational frequencies, and we assess their sensitivity to basis-set choice and relativistic treatment. We find that sc$GW$ yields ionization energies and vibrational properties in very good agreement with experiment and high-accuracy theoretical estimates. For AEA and VDE, diffuse basis sets are essential for convergence. UF is a particularly challenging case for scalar relativistic methods because its electron-attachment and vertical detachment energies are strongly affected by spin--orbit coupling, highlighting the need for a variational two-component treatment. These results establish all-electron X2C-sc$GW$ as a practical route for accurate actinide-molecule energetics and spectroscopy and motivate future applications to larger uranium-containing systems.

physics.chem-ph↗

arXiv2026

Chemically decisive benchmarks on the path to quantum utility

Progress towards quantum utility in chemistry requires not only algorithmic advances, but also the identification of chemically meaningful problems whose electronic structure fundamentally challenges classical methods. Here, we introduce a curated hierarchy of chemically decisive benchmark systems designed to probe distinct regimes of electronic correlation relevant to molecular, bioinorganic, and heavy-element chemistry. Moving beyond minimal toy models, our benchmark set spans multireference bond breaking (N$_2$), high-spin transition-metal chemistry (FeS), biologically relevant iron-sulfur clusters ([2Fe-2S]), and actinide-actinide bonding (U$_2$), which exhibits extreme sensitivity to active-space choice, relativistic treatment, and correlation hierarchy even within advanced multireference frameworks. As a concrete realization, we benchmark a recently developed automated and adaptive quantum algorithm based on generator-coordinate-inspired subspace expansion,ADAPT-GCIM, using a black-box workflow that integrates entropy-based active-space selection via the ActiveSpaceFinder tool. Across this chemically diverse problem set, ADAPT-GCIM achieves high accuracy in challenging correlation regimes. Equally importantly, these benchmarks expose general failure modes and design constraints-independent of any specific algorithm-highlighting the necessity of problem-aware and correlation-specific strategies for treating strongly correlated chemistry on quantum computers. To support systematic benchmarking and reproducible comparisons, the Hamiltonians for all systems studied are made openly available.

physics.chem-ph↗

arXiv2025

Elucidating Many-Body Effects in Molecular Core Spectra through Real-Time Approaches: Efficient Classical Approximations and a Quantum Perspective

Accurately resolving many-body satellite features in molecular core-level spectra requires theoretical approaches that capture electron correlation both efficiently and systematically. The recently developed time-dependent double coupled-cluster (TD-dCC) ansatz achieves this by combining correlation effects from the N- and (N-1)-electron sectors, but its exact formulation remains computationally demanding. Here we introduce a hierarchy of cost-effective approximate TD-dCC ansatzes derived from truncated Baker-Campbell-Hausdorff (BCH) expansions, which preserve a single-similarity-transformation structure while retaining the essential correlation diagrams responsible for satellite formation. We further develop a detailed component analysis that isolates hole-mediated excitation pathways, which are correlated processes arising from the coupling between ground-state and ionized-state amplitudes. We use it to interpret quasiparticle and satellite features across the hierarchy. Applications to the single-impurity Anderson model and molecular systems (H2O and CH4) demonstrate that the approximate TD-dCC methods closely and efficiently reproduce exact many-body spectral features and quasiparticle weights. In parallel, we construct a fault-tolerant quantum signal processing algorithm for the core-hole Green's function, providing a scalable quantum route for simulating correlated core-level dynamics. Together, these developments establish complementary classical and quantum methodologies for quantitative, many-body-accurate core spectroscopy.

quant-ph↗

arXiv2024

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations.

cond-mat.mtrl-sci↗

arXiv2024

Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals

We present a comparison of various approximations to self-consistency in the GW method, including the one-shot G0W0 method, different quasiparticle self-consistency schemes, and the fully self-consistent GW (scGW) approach. To ensure an unbiased and equitable comparison, we have implemented all the schemes with the same underlying Matsubara formalism, while employing Gaussian orbitals to describe the system. Aiming to assess and compare different GW schemes, we analyze band gaps in semiconductors and insulators, as well as ionization potentials in molecules. Our findings reveal that for solids, the different self-consistency schemes perform very similarly. However, for molecules, full self-consistency outperforms all other approximations, i.e., the one-shot and quasiparticle self-consistency GW schemes. Our work highlights the importance of implementation details when comparing different GW methods. By employing state-of-the-art fully self-consistent, finite temperature GW calculations, we have successfully addressed discrepancies in the existing literature regarding its performance. Our results also indicate that when stringent thresholds are imposed, the scGW method consistently yields accurate results.

cond-mat.str-el↗

arXiv2024

Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials

We test the performance of self-consistent GW and several representative implementations of vertex corrected G0W0 (G0W0Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state of the art wave function techniques, our results show that performing full self-consistency in the GW scheme either systematically outperforms vertex corrected G0W0 or gives results of at least the same quality. Moreover, the G0W0Γ results in additional computational cost when compared to G0W0 or self-consistent GW and the G0W0Γ dependency on the starting mean-filed solution is frequently larger than the magnitude of the vertex correction. Consequently, for molecular systems self-consistent GW performed on imaginary axis and then followed by modern analytical continuation techniques offers a more reliable approach to make predictions of IP spectra.

physics.chem-ph↗

arXiv2024

Challenges with relativistic GW calculations in solids and molecules

For molecules and solids containing heavy elements, accurate electronic structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases. Traditionally, the simplest illustration of relativistic effects can be done either by including pseudopotentials in non-relativistic calculations or alternatively by employing large all electron basis sets in relativistic methods. By analyzing different electronic properties (band structure, equilibrium lattice constant and bulk modulus) in semiconductors and insulators, we show that capturing the interplay of relativity and electron correlation can be rather challenging in Green's function methods. For molecular problems with heavy elements, we also observe that similar problems persist. We trace these challenges to three major problems: deficiencies in pseudopotential treatment as applied to Green's function methods, the scarcity of accurate and compact all-electron basis-sets that can be converged with respect to the basis-set size, and linear dependencies arising in all-electron basis-sets particularly when employing Gaussian orbitals. Our analysis provides detailed insight into these problems and opens a discussion about potential approaches to mitigate them.

physics.chem-ph↗

arXiv2024

Relativistic fully self-consistent $GW$ for molecules: Total energies and ionization potentials

The fully self-consistent $GW$ (sc$GW$) method with the iterative solution of Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of sc$GW$ for molecules containing heavy element using the exact two-component (X2C) Coulomb approximation. We benchmark $\texttt{SOC-81}$ dataset containing closed shell heavy elements for the first ionization potential using the fully self-consistent $GW$ as well as one-shot $GW$. The self-consistent $GW$ provides superior result compared to $G_0W_0$ with PBE reference and comparable to $G_0W_0$ with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with experimental spectra. We also observe that sc$GW$ provides very good estimation of ionization potential for the inner $d$ shell orbitals. Additionally, using the well conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of few halogen dimers using sc$GW$. Overall, our findings demonstrate the applicability of the fully self-consistent $GW$ method for accurate ionization potential, photoelectron spectra and total energies in finite systems with heavy elements with a reasonable computational scaling.

physics.chem-ph↗

arXiv2023

Generalization of the tensor product selected CI method for molecular excited states

In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

physics.chem-ph↗

arXiv2023

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H$_2$, H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

quant-ph↗

arXiv2023

Quantum simulation of molecular response properties

Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this paper, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offers a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate state-specific response properties. Further, through noise-less quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster based linear response models due to the improved quality of the ground-state wavefunction obtained using the ADAPT-VQE algorithm.

quant-ph↗

arXiv2022

Coupled electron pair-type approximations for tensor product state wavefunctions

Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional CI methods are not size extensive hence the error increases as the system gets larger. Coupled electron pair approximation (CEPA) methods can be constructed as simple extensions of truncated configuration interaction (CI) that ensures size extensivity. One of the major issues with the CEPA and its variants is that singularities arise in the amplitude equations when the system starts to be strongly correlated. In this work, we extend the traditional Slater determinant-based coupled electron pair approaches like CEPA-0, averaged coupled-pair functional (ACPF) and average quadratic coupled-cluster (AQCC) to a new formulation based on tensor product states (TPS). We show that a TPS basis can often be chosen such that it removes the singularities that commonly destroy the accuracy of CEPA-based methods. A suitable TPS representation can be formed by partitioning the system into separate disjoint clusters and forming the final wavefunction as the tensor product of the many body states of these clusters. We demonstrate the application of these methods on simple bond breaking systems such as CH$_4$ and F$_2$ where determinant based CEPA methods fail. We further apply the TPS-CEPA approach to stillbene isomerization and few planar $π-$conjugated systems. Overall the results show that the TPS-CEPA method can remove the singularities and provide improved numerical results compared to common electronic structure methods.

physics.chem-ph↗

arXiv2021

Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference

The many-body expansion (MBE) is an efficient tool which has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. In the past, applications of MBE to correlation energy have been unfeasible for large systems, but recent improvements to computing resources have sparked renewed interest in capturing the correlation energy using the generalized $n$-th order Bethe-Goldstone equation. In this work, we extend this approach, originally proposed for a Slater determinant, to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean field reference TPS configuration and includes the correlation contribution of the excited TPSs using the many-body expansion. This method, named cluster many-body expansion (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block based MBE from a RHF reference. We present numerical results for strongly correlated systems such as the one- and two-dimensional Hubbard models and the chromium dimer. The performance of the cMBE method is also tested by partitioning the extended $π$ space of several large $π$-conjugated systems, including a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require $10^{66}$ determinants for the exact FCI solution.

cond-mat.str-el↗

arXiv2020

Selected Configuration Interaction in a Basis of Cluster State Tensor Products

Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces, compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: 1) modified Hubbard model with different inter- and intra-cluster hopping terms, 2) less obviously clusterable cases of bond breaking in N2 and F2, and 3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.

cond-mat.str-el↗