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Journal of Chemical Theory and Computation

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

Anthony Gandon, Alberto Baiardi, Pauline J. Ollitrault, Ivano Tavernelli

Published Jul 5, 2024• 12 citations
Publisher

Abstract

We introduce a novel computational framework for excited-state molecular quantum dynamics simulations driven by quantum-computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the nonadiabatic effects that tune the reactive event.

DOI
10.1021/acs.jctc.4c00233

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We introduce a novel computational framework for excited-state molecular quantum dynamics simulations driven by quantum-computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the nonadiabatic effects that tune the reactive event.
We introduce a novel computational framework for excited-states molecular quantum dynamics simulations driven by quantum computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics, and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the non-adiabatic effects that tune the reactive event.
Investigating ultrafast electron-nuclear dynamics in molecules requires robust theoretical methods that offer predictive capabilities beyond interpretation purposes. However, the vast number of electronic and nuclear degrees of freedom often prevents an accurate description of chemical systems on classical computers. To address these challenges, hybrid approaches combining quantum and classical computing can leverage the strengths of both to enhance the computational efficiency and fully exploit hardware capabilities. In this work, we perform excited-state molecular dynamics simulations of the formaldimine molecule by combining the surface hopping nonadiabatic molecular dynamics technique with quantum algorithms. We replace conventional electronic energy and overlap calculations with the variational quantum deflation (VQD) algorithm and the Hadamard test, respectively, employing a configuration state function (CSF) spin-restricted ansatz. Finally, we evaluate the accuracy and feasibility of three different gradient calculation approaches integrated with the quantum computing components, demonstrating the advantages of an analytical gradient method over finite difference approaches for hybrid quantum-classical integration.
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general mathematical framework that describes how quantum computers can efficiently explore molecular potential energy surfaces through iterative subspace construction. Our theory characterizes the relationship between subspace dimension, basis set selection, and solution accuracy for ground and excited state calculations. We derive analytical expressions for the number of quantum measurements required to achieve chemical accuracy and establish conditions under which quantum subspace methods offer polynomial advantages over classical approaches. The framework incorporates realistic noise models, providing performance predictions for near-term quantum devices. We analyze trade-offs between circuit depth, measurement overhead, and solution quality, identifying optimal operating regimes for different molecular systems. Special attention is devoted to transition-state mapping for chemical reactions, where we prove that adaptive subspace selection achieves exponential reduction in required measurements compared to uniform sampling. Applications to battery electrolyte reactions, drug discovery, and materials design demonstrate the practical utility of our theoretical predictions. This work establishes quantum subspace methods as a rigorous alternative to variational approaches, offering theoretical guarantees absent in parameter-optimization-based algorithms while maintaining compatibility with near-term quantum hardware constraints.
We propose an excited-state molecular dynamics simulation method based on variational quantum algorithms at a computational cost comparable to that of ground-state simulations. We utilize the feature that excited-states can be obtained as metastable states in the restricted variational quantum eigensolver calculation with a hardware-efficient ansatz. To demonstrate the effectiveness of the method, molecular dynamics simulations are performed for the S1 excited-states of H2 and CH2NH molecules. The results are consistent with those of the exact adiabatic simulations in the S1 states, except for the CH2NH system, after crossing the conical intersection, where the proposed method causes a nonadiabatic transition.
Abstract In this Perspective, we discuss how quantum computers may advance the simulation of nonadiabatic molecular dynamics, a framework central to describing excited-state processes in photochemistry, biology, and materials science. Classical approaches span from exponentially scaling full quantum dynamics to more approximate mixed quantum–classical techniques such as surface hopping and Ehrenfest dynamics. Hybrid quantum–classical algorithms – particularly those based on the variational quantum eigensolver – offer a transformative alternative by providing access to the key electronic properties needed to drive nonadiabatic molecular dynamics simulations, including energies, gradients, and nonadiabatic couplings. We examine recent proof-of-principle quantum simulations of reduced model systems which, despite being restricted to small molecules and limited active spaces due to constraints of qubit number and device noise, already showcase the potential of quantum devices to capture phenomena such as conical intersections and ultrafast relaxation. Although practical applications are not yet feasible in the present noisy intermediate-scale quantum era, these efforts underline the conceptual and methodological advances of quantum algorithms paving the way for large-scale quantum simulations of nonadiabatic processes. Framed within the 2025 International Year of Quantum Science and Technology, such progress exemplifies how quantum computing may open new horizons for chemistry and beyond.
Nuclear quantum effects are critical for describing proton transfer and hydrogen bonding, but their incorporation into quantum chemistry calculations is often computationally prohibitive on classical hardware. A promising alternative are quantum computers due to their linear scaling in the space requirements with system size. We introduce a novel hybrid quantum-classical algorithm for ab-initio molecular dynamics that incorporates nuclear quantum effects via the nuclear-electronic orbital method. The proposed algorithm evaluates ground state energies and forces on the quantum computer using a variational quantum eigensolver, while the molecular geometries are updated classically. We validate our approach through simulations of H2\text{H}_2H2​, H2O\text{H}_2\text{O}H2​O and the Zundel ion H5O2+\text{H}_5\text{O}_2^+H5​O2+​, comparing the simulated vibrational spectra with experimental data. Upon inclusion of nuclear quantum effects, the proton shuttling movement in the Zundel ion becomes effectively barrierless, and errors in the simulated frequencies improve significantly. Employing compact hardware-efficient ansatz circuits we achieve results comparable to the more accurate UCCSD ansatzes, which hints towards the feasibility of executing our algorithm on near-term quantum devices.