Constrained Nuclear-Electronic Orbital Theory for Quantum Computation
Tanner Culpitt, Zehua Chen, Fabijan Pavošević, Yang Yang · Journal of Chemical Theory and Computation · 2025
Quantum computing offers promising advantages for computational chemistry, particularly through algorithms that efficiently model correlated methods. In this work, we apply quantum computing techniques to the constrained nuclear-electronic orbital (CNEO) framework, which enables the inclusion of nuclear quantum effects in chemical simulations while preserving a well-defined molecular structure. We present the development and implementation of two correlated wave function methods within this framework: CNEO full configuration interaction (CNEO-FCI) and CNEO unitary coupled-cluster with singles and doubles (CNEO-UCCSD), with the latter solved using the variational quantum eigensolver algorithm. These methods were applied to the hydrogen isotopologues H 2, HD, and D 2 and used to calculate potential energy surfaces, equilibrium geometries, harmonic vibrational frequencies, and von Neumann entropies. The CNEO-UCCSD results are in excellent agreement with CNEO-FCI, recovering over 99% of the correlation energy and accurately capturing geometries and vibrational frequencies. Additionally, we observe a strong connection between CNEO-FCI and CNEO-UCCSD energy and entropy differences as a function of bond length, highlighting the role of quantum entanglement in molecular dissociation. These results demonstrate the viability of CNEO-based quantum algorithms for capturing nuclear quantum effects and lay the groundwork for future quantum simulations and entropy analysis of multicomponent systems within the CNEO paradigm.