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Physical Review C

Ab initio many-fermion structure calculations on a quantum computer

Weijie Du, Yang-Guang Yang, Zi Xin Liu, Chao Yang, James P. Vary

Published May 21, 2026• 0 citations
Publisher
DOI
10.1103/1spg-5ld3

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We propose introducing an extended Hubbard Hamiltonian derived via the ab initio downfolding method, which was originally formulated for periodic materials, toward efficient quantum computing of molecular electronic structure calculations. By utilizing this method, the first-principles Hamiltonian of chemical systems can be coarse-grained by eliminating the electronic degrees of freedom in higher energy space and reducing the number of terms of electron repulsion integral from O(N4) to O(N2). Our approach is validated numerically on the vertical excitation energies and excitation characters of ethylene, butadiene, and hexatriene. The dynamical electron correlation is incorporated within the framework of the constrained random phase approximation in advance of quantum computations, and the constructed models capture the trend of experimental and high-level quantum chemical calculation results. As expected, the L1-norm of the fermion-to-qubit mapped model Hamiltonians is significantly lower than that of conventional ab initio Hamiltonians, suggesting improved scalability of quantum computing. Those numerical outcomes and the results of the simulation of excited-state sampling demonstrate that the ab initio extended Hubbard Hamiltonian may hold significant potential for quantum chemical calculations using quantum computers.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann–Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.
The structure and energetics of (3,4)HeCs(2)((3)Sigma(u)) molecules are analyzed from first principles. Fixing the cesium dimer at its equilibrium distance, the electronic structure was determined through ab initio methods at the CCSD(T) level of theory using a large basis set to compute the interaction energies. At the T-shaped geometry, there is a shallow well with a depth of approximately 2 cm(-1) placed at R approximately 6.75 A, R being the distance from the center of mass of Cs(2) to He. That depth gradually decreases to approximately 0.75 cm(-1), while R increases to about 11.5 A at linear arrangements. A simple model of adding atom-atom Lennard-Jones potentials with well-depth and equilibrium distance parameters depending on the angular orientation was found to accurately reproduce the ab initio points. Using this analytical form, variational calculations at zero total angular momentum are performed, predicting a single bound level at approximately -0.106 (approximately -0.042) cm(-1) for the boson (fermion) species. Further calculations using Quantum Monte Carlo methods are carried out and found to be in good agreement with the variational ones. On the basis of the present results, such analytical expression could in turn be used to describe the structure and binding of larger complexes and therefore opens the possibility to further studies involving such aggregates.