The authors demonstrate the efficacy of the quantum phase estimator algorithm for evaluating the spectral function related to the ionization-potential part of a one-electron Green's function in the high-energy regime. They assess the algorithm's accuracy by comparing it to results derived from both exact and approximate formulations that incorporate high-rank correlation effects.
The authors demonstrate the efficacy of the quantum phase estimator algorithm for evaluating the spectral function related to the ionization-potential part of a one-electron Green's function in the high-energy regime. They assess the algorithm's accuracy by comparing it to results derived from both exact and approximate formulations that incorporate high-rank correlation effects.
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.
Quantum Simulation of Many-Body Effects in the Li−, Be, and B+ Isoelectronic Systems using the Variational Quantum Eigensolver Algorithm
The emerging field of quantum simulation of many-body systems is widely recognized as a killer application of quantum computing. A crucial step towards realizing its full potential requires understanding the role of electron correlation effects that lie at the heart of such calculations. In this pilot study, we investigate the trends in the electron correlation effects in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver (VQE) algorithm. To facilitate a comparative analysis, we consider three isoelectronic systems, namely Li−, Be, and B+, that is, an anion, a neutral atom and a cation, respectively. We choose the unitary coupled-cluster (UCC) ansatz for our computations. We conduct a rigorous analysis of the factors that could affect the accuracy with which electron correlation effects can be captured, namely mappings, backend simulators, and basis sets. The obtained results are also compared with those calculated by using the full configuration interaction method, coupled-cluster theory and UCC method, on a classical computer. A noteworthy part of the study involves a careful analysis to find the number of shots required for calculations with Qiskit's QASM simulator backend, which mimics an ideal quantum computer, at which one can obtain results in very good agreement with those from a classical computer.
We investigate analytically the performance of many-body energy functionals, derived by Klein, Luttinger, and Ward, at different levels of diagrammatic approximations, ranging from second Born, to , to the so-called T matrix, for the calculation of total energies and potential energy surfaces. We benchmark our theoretical results on the extended two-site Hubbard model, which is analytically solvable and for which several exact properties can be calculated. Despite its simplicity, this model displays the physics of strongly correlated electrons: it is prototypical of the H 2 dissociation, a notoriously difficult problem to solve accurately for the majority of mean-field-based approaches. We show that both functionals exhibit good to excellent variational properties, particularly in the case of the Luttinger-Ward one, which is in close agreement with fully self-consistent calculations, and we elucidate the relation between the accuracy of the results and the different input one-body Green's functions. Provided that these are wisely chosen, we show how the Luttinger-Ward functional can be used as a computationally inexpensive alternative to fully self-consistent many-body calculations, without sacrificing the precision of the results obtained. Furthermore, in virtue of this accuracy, we argue that this functional can also be used to rank different many-body approximations at different regimes of electronic correlation, once again bypassing the need for self-consistency. Published by the American Physical Society 2024
This paper explores the utility of the quantum phase estimation (QPE) algorithm in calculating high-energy excited states characterized by the promotion of electrons occupying core-level shells. These states have been intensively studied over the last few decades, especially in supporting the experimental effort at light sources. Results obtained with QPE are compared with various high-accuracy many-body techniques developed to describe core-level states. The feasibility of the quantum phase estimator in identifying classes of challenging shake-up states characterized by the presence of higher-order excitation effects is discussed. We also demonstrate the utility of the QPE algorithm in targeting excitations from specific centers in a molecule. Lastly, we discuss how the lowest-order Trotter formula can be applied to reducing the complexity of the ansatz without affecting the error.
The necessity to determine the static self-energy part Σ(∞) in many-body Green’s function studies of atomic and molecular ionization introduces difficulties affecting both the accuracy and the efficiency of the method. We show how this bottleneck can be overcome under an approximation obtained by truncating the Dyson expansion for the one-particle Green’s function G(ω). Here the essential computational step consists of an inversion or a Lanczos diagonalization of constant Hermitian secular matrices associated with the dynamical self-energy part M(ω). Both methods are very practical and efficient as is demonstrated in an exemplary application to the CO molecule. The same approximation and numerical techniques apply also to the problem of extracting ground state information from G(ω), i.e., correlation energy and expectation values of single-particle operators.
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.