In this work, we explore the implementation possibility of quantum simulation for quantum molecular dynamics, in particular for reaction dynamics, though several implementations have already reported through quantum-classical mixed simulations ({\it Acc. Chem. Res.} {\bf 54} (2021), 4229 and {\it J. Phys. Chem. Lett.} {\bf xx} (2026), XXXX). To analyze this aspect, we examine (1) the conjugacy relation between quantum simulator and the target molecular system, (2) the wave function correspondence in quantum algorithm and classical algorithm for multi-dimensional dynamics, (3) problems arisen from real-valued classical algorithms, and finally (4) geometric phase arisen from the separation among the degrees of freedom (DOFs). As is well known, the aforementioned first and second points play fundamental roles in quantum simulation of quantum many-body systems, and the third and fourth points are theoretical issues that might introduce problems in classical and quantum computing. In this work, we mainly focus on the third and fourth points by analysis of the first two points by reviewing previously reported quantum-classical mixed implementations of quantum simulation. We also consider gauge freedom in high-dimensional quantum molecular dynamics that has been introduced recently, and then discuss possibility of advantages and disadvantages of quantum simulation for molecular reaction dynamics.
In this work, we explore the implementation possibility of quantum simulation for quantum molecular dynamics, in particular for reaction dynamics, though several implementations have already reported through quantum-classical mixed simulations ({\it Acc. Chem. Res.} {\bf 54} (2021), 4229 and {\it J. Phys. Chem. Lett.} {\bf xx} (2026), XXXX). To analyze this aspect, we examine (1) the conjugacy relation between quantum simulator and the target molecular system, (2) the wave function correspondence in quantum algorithm and classical algorithm for multi-dimensional dynamics, (3) problems arisen from real-valued classical algorithms, and finally (4) geometric phase arisen from the separation among the degrees of freedom (DOFs). As is well known, the aforementioned first and second points play fundamental roles in quantum simulation of quantum many-body systems, and the third and fourth points are theoretical issues that might introduce problems in classical and quantum computing. In this work, we mainly focus on the third and fourth points by analysis of the first two points by reviewing previously reported quantum-classical mixed implementations of quantum simulation. We also consider gauge freedom in high-dimensional quantum molecular dynamics that has been introduced recently, and then discuss possibility of advantages and disadvantages of quantum simulation for molecular reaction dynamics.
Quantum computers could potentially simulate the dynamics of systems such as polyatomic molecules on a much larger scale than classical computers. One of the central unresolved problems in developing quantum simulation algorithms has been constructing the necessary time evolution operators in enough detail for implementation in a quantum computer. This work presents a complete and very general solution to this problem: namely, a quantum computational algorithm for simulating an arbitrary Coulombic many-body system acting under the three-dimensional Schrödinger equation. We use the simplest discretized model and discuss detailed constructions of the operators involved. The algorithm is also implemented in MAT-LAB and tested against both analytical solutions and classical methods. Our algorithm can determine an arbitrary system’s dynamics rather than merely associated constants, as investigated in previous literature. It can hence be adapted for electronic structure calculations, chemical reaction simulations, etc. 1
ConspectusSimulating molecular dynamics (MD) within a comprehensive quantum framework has been a long-standing challenge in computational chemistry. An exponential scaling of computational cost renders solving the time dependent Schrödinger equation (TDSE) of a molecular Hamiltonian, including both electronic and nuclear degrees of freedom (DOFs), as well as their couplings, infeasible for more than a few DOFs. In the Born-Oppenheimer (BO), or adiabatic, picture, electronic and nuclear parts of the wave function are decoupled and treated separately. Within this framework, the nuclear wave function evolves along potential energy surfaces (PESs) computed as solutions to the electronic Schrödinger equation parametrized in the nuclear DOFs. This approximation, together with increasingly elaborate numerical approaches to solve the nuclear time dependent Schrödinger equation (TDSE), enabled the treatment of up to a few dozens of degrees of freedom (DOFs). However, for particular applications, such as photochemistry, the BO approximation breaks down. In this regime of non-adiabatic dynamics, solving the full molecular problem including electron-nuclear couplings becomes essential, further increasing the complexity of the numerical solution. Although valuable methods such as multiconfigurational time-dependent Hartree (MCTDH) have been proposed for the solution of the coupled electron-nuclear dynamics, they remain hampered by an exponential scaling in the number of nuclear DOFs and by the difficulty of finding universal variational forms.In this Account, we present a perspective on novel quantum computational algorithms, aiming to alleviate the exponential scaling inherent to the simulation of many-body quantum dynamics. In particular, we focus on the derivation and application of quantum algorithms for adiabatic and non-adiabatic quantum dynamics, which include efficient approaches for the calculation of the BO potential energy surfaces (PESs). Thereafter, we study the time-evolution of a model system consisting of two coupled PESs in first and second quantization. In a first application, we discuss a recently introduced quantum algorithm for the evolution of a wavepacket in first quantization and exploit the potential quantum advantage of mapping its spatial grid representation to logarithmically many qubits. For the second demonstration, we move to the second quantization framework and review the scaling properties of two alternative time-evolution algorithms, namely, a variational quantum algorithm (VQA) (based on the McLachlan variational principle) and conventional Trotter-type evolution (based on a Lie-Trotter-Suzuki formula). Both methods clearly demonstrate the potential of quantum algorithms and their favorable scaling compared to the available classical approaches. However, a clear demonstration of quantum advantage in the context of molecular quantum dynamics may require the implementation of these algorithms in fault-tolerant quantum computers, while their application in near-term, noisy quantum devices is still unclear and deserves further investigation.
This research explores the potential of quantum simulation for tackling complex molecular dynamics problems that are currently intractable for classical computers. The core idea involves leveraging the principles of quantum mechanics to model molecular systems, specifically focusing on simulating the dynamic behavior of molecules and their interactions. We propose a framework for constructing a quantum simulator utilizing quantum bits (qubits) to represent and evolve molecular states. The theoretical framework presented herein outlines the methodology for mapping molecular dynamics problems onto a quantum computational platform, highlighting the advantages and challenges associated with this approach. Specifically, we examine the impact of quantum effects, such as superposition and entanglement, on the simulation accuracy and efficiency. This work contributes to the nascent field of quantum molecular dynamics and provides a foundation for future investigations into the development of practical quantum simulation tools. The key objective is to demonstrate that quantum simulation, when properly implemented, can significantly outperform classical methods for simulating complex molecular systems, particularly those involving significant quantum effects.
It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.
Accurately simulating molecular dynamics during chemical reactions remains a central challenge in computational chemistry. These processes are inherently quantum mechanical, involving coupled electronic and nuclear motion and non-adiabatic effects. A fully quantum description is therefore required, yet the associated computational cost grows exponentially with system size. Even with modern supercomputers, storing and evolving a molecular wavefunction rapidly becomes intractable, limiting exact simulations of chemical dynamics. Quantum simulation offers a promising alternative by using controllable quantum systems to directly reproduce molecular dynamics. However, fully digital, qubit-based approaches remain impractical for chemistry due to limited qubit numbers, coherence times, and gate fidelities. This motivates the exploration of more resource-efficient quantum architectures. In this thesis, we demonstrate that mixed-qudit-boson (MQB) quantum simulators provide a practical platform for simulating chemical dynamics in the quantum regime. In MQB devices, multilevel qudits encode electronic states while bosonic modes natively represent vibrational degrees of freedom, avoiding costly qubit encodings of nuclear motion and substantially reducing resource requirements. The thesis makes three main contributions. First, it reports the direct observation of geometric-phase interference in non-adiabatic dynamics using an MQB simulation of the Jahn–Teller model. Second, it extends the MQB framework to open-system chemical dynamics through programmable Lindblad dissipation. Third, it presents a resource analysis showing that MQB simulators can reduce resource costs by several orders of magnitude relative to qubit-only approaches. Together, these results establish MQB quantum simulators as a promising route for studying chemical dynamics beyond the reach of classical computation.
Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.