Massively Parallel Implementation of Explicitly Correlated Coupled-Cluster Singles and Doubles Using TiledArray Framework

A new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical <i>O</i>(<i>N</i>⁶) computational complexity is described. The implementation is based on the TiledArray tensor framework. Novel features of the implementation include (a) all data greater than <i>O</i>(<i>N</i>) is distributed in memory and (b) the mixed use of density fitting and integral-driven formulations that optionally allows to avoid storage of tensors with three and four unoccupied indices. Excellent strong scaling is demonstrated on a multicore shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. The performance on a shared-memory computer is competitive with the popular CCSD implementations in ORCA and Psi4. Moreover, the CCSD performance on a commodity-size cluster significantly improves on the state-of-the-art package NWChem. The large-scale parallel explicitly correlated coupled-cluster implementation makes routine accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms. Thus, it can provide valuable benchmarks for the merging reduced-scaling coupled-cluster approaches. The new implementation allowed us to revisit the basis set limit for the CCSD contribution to the binding energy of π-stacked uracil dimer, a challenging paradigm of π-stacking interactions from the S66 benchmark database. The revised value for the CCSD correlation binding energy obtained with the help of quadruple-ζ CCSD computations, −8.30 ± 0.02 kcal/mol, is significantly different from the S66 reference value, −8.50 kcal/mol, as well as other CBS limit estimates in the recent literature

Toward Accurate Post-Born–Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born–Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO methodan important step toward accurate simulations involving nonclassical nuclei and non-Born–Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes