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.
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.
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.
The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.
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, H2O and the Zundel ion H5O2+, 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.
Nuclear quantum phenomena beyond the Born-Oppenheimer approximation are known to play an important role in a growing number of chemical and biological processes. While there exists no unique consensus on a rigorous and efficient implementation of coupled electron-nuclear quantum dynamics, it is recognized that these problems scale exponentially with system size on classical processors and, therefore, may benefit from quantum computing implementations. Here, we introduce a methodology for the efficient quantum treatment of the electron-nuclear problem on near-term quantum computers, based upon the Nuclear-Electronic Orbital (NEO) approach. We generalize the electronic two-qubit tapering scheme to include nuclei by exploiting symmetries inherent in the NEO framework, thereby reducing the Hamiltonian dimension, number of qubits, gates, and measurements needed for calculations. We also develop parameter transfer and initialization techniques, which improve convergence behavior relative to conventional initialization. These techniques are applied to H2 and malonaldehyde for which results agree with NEO full configuration interaction and NEO complete active space configuration interaction benchmarks for ground state energy to within 10-6 hartree and entanglement entropy to within 10-4. These implementations therefore significantly reduce resource requirements for full quantum simulations of molecules on near-term quantum devices while maintaining high accuracy.
Non-adiabatic dynamics at molecule-metal interfaces govern diverse and technologically important phenomena, from heterogeneous catalysis to dye-sensitized solar energy conversion and charge transport across molecular junctions. Realistic modeling of such dynamics necessitates taking into account various charge and energy transfer channels involving the coupling of nuclear motion with a very large number of electronic states, leading to prohibitive cost using classical computational methods. In this work we introduce a generalization of the Anderson-Newns Hamiltonian and develop a highly optimized quantum algorithm for simulating the non-adiabatic dynamics of realistic molecule-metal interfaces. Using the PennyLane software platform, we perform resource estimations of our algorithm, showing its remarkably low implementation cost for model systems representative of various scientifically and industrially relevant molecule-metal systems. Specifically, we find that time evolution for models including 100 metal orbitals, 8 molecular orbitals, and 20 nuclear degrees of freedom, requires only 271 qubits and 7.9×107 Toffoli gates for 1000 Trotter steps, suggesting non-adiabatic molecule-metal dynamics as a fruitful application of first-generation fault-tolerant quantum computers.
without the separation of electrons and nuclei, by mapping the molecular Hamiltonian to a device with coupled qubits and bosonic modes. We perform a proof-of-principle emulation of our ansatz using a single-mode model system which represents vibronic dynamics of chemical systems, such as nonadiabatic charge transfer involving polarization of the medium, and propose an implementation of our approach on a trapped-ion device. We show that our approach has exponential savings in resource and computational costs compared to the equivalent classical algorithms. Furthermore, our approach has a much smaller resource and implementation scaling than the existing pre-BO quantum algorithms for chemical dynamics. The low cost of our approach will enable an exact treatment of electron-nuclear dynamics on near-term quantum devices.