Coupled-cluster-equations for the local ansatz

Karol Kowalski

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

Isaiah Shavitt, Rodney J. Bartlett

Bo Peng, Himadri Pathak, Ajay Panyala +3 more

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.

Mark Jarrell

Bo Peng, Karol Kowalski

Nonunitary theories are commonly seen in the classical simulations of quantum systems. Among these theories, the method of moments of coupled cluster equations (MMCCs) and the ensuing classes of the renormalized coupled cluster (CC) approaches have evolved into one of the most accurate approaches to describe correlation effects in various quantum systems. The MMCC formalism provides an effective way for correcting the energies of approximate CC formulations (parent theories) using moments, or CC equations, that are not used to determine approximate cluster amplitudes. In this paper, we propose a quantum algorithm for computing MMCC ground-state energies that provides two main advantages over classical computing or other quantum algorithms: (i) the possibility of forming superpositions of CC moments of arbitrary ranks in the entire Hilbert space and using an arbitrary form of the parent cluster operator for MMCC expansion, and (ii) significant reduction in the number of measurements in quantum simulation through a compact unitary representation for a generally nonunitary operator. We illustrate the robustness of our approach over a broad class of test cases, including $\ensuremath{\sim}40$ molecular systems with varying basis sets encoded using 4--40 qubits, and we exhibit the detailed MMCC analysis for the 8-qubit half-filled, four-site, single impurity Anderson model and the 12-qubit hydrogen fluoride molecular system from the corresponding noise-free and noisy MMCC quantum computations. We also outline the extension of the MMCC formalism to the case of a unitary CC wave-function Ansatz.

Isaiah Shavitt, Rodney J. Bartlett