Nonadiabatic Nuclear–Electron Dynamics: A Quantum Computing Approach

Abstract

Coupled quantum electron−nuclear dynamics is often associated with the Born−Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

Nonadiabatic Molecular Dynamics with Fermionic Subspace-Expansion Algorithms on Quantum Computers

“…Alternatively, it can be combined with a multicomponent electron–nuclear quantum dynamics such as Nuclear-Electronic Orbital (NEO) framework . In the first case, one can possibly leverage quantum hardware to speed up the vibrational dynamics itself, , while efficient quantum computing implementations of the NEO algorithms have already shown promising results. , …”

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

“…We expect that due to constant improvements of quantum hardware efficiency and the demonstrated accuracy of q-NEO-FNO-ADAPT, the latter will play a central role in future implementations and non-Born−Oppenheimer simulations on near-term quantum devices. In particular, it presents a promising approach for simulating the dynamics of tautomeric isomerization reactions introduced in ref 42. By employing q-NEO-FNO-ADAPT alongside variational time-evolution methods, 71 one can simulate these reactions in both adiabatic and nonadiabatic regimes using short, constant-size quantum circuits.…”

“…40 This study demonstrated that the NEO-UCC/VQE ground-and excited-state energies for these two systems are in excellent agreement with the exact (full CI) energies. 40 Following that work, qubit tapering and ansatz parameter initialization procedures were introduced, 41 eventually leading to the development of an approach 42 to simulate proton transfer dynamics. The first impediment to the discussed simulations is that they are limited to minimal or near-minimal electronic and nuclear basis sets.…”

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy

“…An early demonstration of quantum speed-up in the simulation of unitary quantum dynamics was proposed by Lloyd . More recently, several sophisticated protocols have been developed for simulating the dynamics of molecular systems. − In this work, we build on the established advantage of quantum simulation of field-free many-body Hamiltonian dynamics and focus on the algorithm connecting such dynamics to the simulation of spectral features in linear and nonlinear optical techniques. To this aim, we leverage the structure of the response function as a linear combination of Time Correlation Functions (TCFs) of the dipole moment operator of the system.…”

“…For example, it is possible to employ a stochastic propagation of the state vector exploiting the repetition of the quantum circuit due to sampling, as demonstrated in the context of the simulation of exciton transport with digital QCs . Indeed, this method has already proven effective in designing resource-efficient algorithms for classical computers. , Alternatively, other quantum algorithms to simulate open system dynamics of excitonic systems have been proposed , including an explicit representation of the environment through the use of a collision model or by inserting vibrational degrees of freedom to follow the wavepacket dynamics in the excited state. , For multidimensional spectra, scanning of delay times represents a particularly demanding computational task in both classical and quantum simulations. To reduce the computational burden, strategies already implemented in experiments, such as compressed sensing techniques, − may aid in effectively reducing the number of sampled points.…”