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.
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.
Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects requires formalisms that provide a hierarchical infrastructure of approximations. These approximations lead to an increased overhead in classical computing methods, and therefore, decisions regarding the ranking of approximations and the quality of results must be made on purely numerical grounds. The emergence of quantum computing methods has the potential to change this situation. In this study, we demonstrate the efficiency of Quantum Phase Estimator (QPE) in identifying core-level states relevant to x-ray photoelectron spectroscopy. We compare and validate the QPE predictions with exact diagonalization and real-time equation-of-motion coupled cluster formulations, which are some of the most accurate methods for states dominated by collective correlation effects.
In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green's function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green's function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green's function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green's function approach and other Green's function approaches in the numerical exact limit.
NISQ era devices suffer from a number of challenges like limited qubit connectivity, short coherence times and sizable gate error rates. Thus, quantum algorithms are desired that require shallow circuit depths and low qubit counts to take advantage of these devices. We attempt to realize this with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically through an approximate similarity transformation of the Hamiltonian with a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorelated Hamiltonians are able to describe both ground and excited states of molecular systems in a balanced manner. Using the fermionic-ADAPT-VQE method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the much larger cc-pVTZ basis. This leads to a potential reduction in the number of required CNOT gates by more than three orders of magnitude for the chemical species studied in this work. Furthermore, using the qEOM formalism in conjunction with the transcorrelated Hamiltonian, we reduce the errors in excitation energies by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.
Strong/static electronic correlation mediates the emergence of remarkable phases of matter, and underlies the exceptional reactivity properties in transition metal-based catalysts. Modeling strongly correlated molecules and solids calls for multi-reference Ansätze, which explicitly capture the competition of energy scales characteristic of such systems. With the efficient computational screening of correlated solids in mind, the ghost Gutzwiller (gGut) Ansatz has been recently developed. This is a variational Ansatz which can be formulated as a self-consistent embedding approach, describing the system within a non-interacting, quasiparticle model, yet providing accurate spectra in both low and high energy regimes. Crucially, small fragments of the system are identified as responsible for the strong correlation, and are therefore enhanced by adding a set of auxiliary orbitals, the ghosts. These capture many-body correlations through one-body fluctuations and subsequent out-projection when computing physical observables. gGut has been shown to accurately describe multi-orbital lattice models at modest computational cost. In this work, we extend the gGut framework to strongly correlated molecules, for which it holds special promise. Indeed, despite the asymmetric embedding treatment, the quasiparticle Hamiltonian effectively describes all major sources of correlation in the molecule: strong correlation through the ghosts in the fragment, and dynamical correlation through the quasiparticle description of its environment. To adapt the gGut Ansatz for molecules, we address the fact that, unlike in the lattice model previously considered, electronic interactions in molecules are not local. Hence, we explore a hierarchy of approximations of increasing accuracy capturing interactions between fragments and environment, and within the environment, and discuss how these affect the embedding description of correlations in the whole molecule. We will compare the accuracy of the gGut model with established methods to capture strong correlation within active space formulations, and assess the realistic use of this novel approximation to the theoretical description of correlated molecular clusters.
We present a molecular extension of our recently proposed Green’s function embedding method, interacting-bath dynamical embedding theory (ibDET), for computing charged excitation energies at the GW and EOM-CCSD levels. Starting from atom-centered impurities, we construct bath representations that capture the frequency-dependent entanglement between the impurity and its environment and can be systematically improved via the construction of cluster-specific natural orbitals. Utilizing a GW or coupled-cluster Green’s function solver, the self-energy of the full system is assembled from all embedding problems to obtain the interacting Green’s function. We show that ibDET provides accurate spectral properties with much reduced cost for a broad range of systems, including conjugated molecules and nanoclusters. Compared with full-system results, the errors in the predicted ionization potentials and electron affinities are around 0.1 eV or smaller, while each embedding problem includes only a small fraction of the total orbital space. This work provides an efficient and scalable framework for computing spectral properties of molecular systems.