Quantum dynamics calculations scale steeply with system size, rendering calculations on a classical computer intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics has been scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wave function is propagated via a split-operator method, utilizing the quantum Fourier transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a nonunitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the autocorrelation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating its promise for application of noisy devices for quantum dynamics studies.
Quantum dynamics calculations scale steeply with system size, rendering calculations on a classical computer intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics has been scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wave function is propagated via a split-operator method, utilizing the quantum Fourier transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a nonunitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the autocorrelation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating its promise for application of noisy devices for quantum dynamics studies.
Theoretical quantum dynamics calculations scale deeply with system size, rendering classical calculations intractable for complex systems. While quantum computing offers a natural solution, its application to nuclear quantum dynamics remains scarce. Here, we present a quantum algorithm to study photodissociation dynamics on quantum computers, benchmarked on the NOCl molecule. The wavefunction is propagated via a split-operator method, utilizing the Quantum Fourier Transform and unitary transformation matrix to switch representations. To impose outgoing boundary conditions on a truncated grid, we use a non-unitary absorbing potential propagator, implemented through a dilation scheme. The photodissociation cross section is calculated from the auto-correlation function, which is extracted using the Hadamard test. Our quantum computing results agree well with benchmarks under ideal conditions, and we further demonstrate that the algorithm is robust to noise and statistical sampling errors, indicating the promising application of noisy devices to quantum dynamics studies.
In this work, we investigate the capability of known quantum computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics of excitation and ionization processes in small molecules such as lithium hydride, which can be benchmarked against the most accurate time-dependent full configuration interaction (TD-FCI) calculations. The conventional TD-FCI wave packet propagation is reproduced using the Jordan-Wigner transformation for wave function and operators and the Trotter product formula for expressing the propagator. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. To include non-Hermitian operators in the ionization dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator, including a complex absorption potential, into quantum gates. The computations are executed on a quantum computer simulator. By construction, all quantum computer algorithms, except for the QITE algorithm used only for ionization but not for excitation dynamics, would scale polynomially on a quantum computer with fully entangled qubits. In contrast, TD-FCI scales exponentially. Hence, quantum computation holds promises for substantial progress in the understanding of electron dynamics of excitation processes in increasingly large molecular systems, as has already been witnessed in electronic structure theory.
In this work, we investigate the capability of known quantum-computing algorithms for fault-tolerant quantum computing to simulate the laser-driven electron dynamics in small molecules such as lithium hydride. These computations are executed on a quantum-computer simulator. Results are compared with the time-dependent full configuration interaction method (TD-FCI). The actual wave packet propagation is closely reproduced using the Jordan-Wigner transformation and the Trotter product formula. In addition, the time-dependent dipole moment, as an example of a time-dependent expectation value, is calculated using the Hadamard test. In order to include non-Hermitian operators in the dynamics, a similar approach to the quantum imaginary time evolution (QITE) algorithm is employed to translate the propagator into quantum gates. Thus, ionization of a hydrogen molecule under the influence of a complex absorbing potential can be simulated accurately. All quantum computer algorithms used scale polynomially rather than exponentially as TD-FCI and therefore hold promise for substantial progress in the understanding of electron dynamics of increasingly large molecular systems in the future.
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.
Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks down. Quantum computers could simulate quantum-chemical dynamics more efficiently than classical computers, but there is currently no complete quantum algorithm for calculating dynamical observables to within a known error. Here, we develop an efficient, end-to-end quantum algorithm for simulating chemical dynamics that avoids all uncontrolled approximations (including the Born-Oppenheimer approximation) and whose error is bounded subject to mild assumptions. To do so, we treat the nuclei and the electrons on an equal footing and simulate the full molecular wavefunction on a momentum-space grid in first quantization, including all algorithmic steps: initial-state preparation, time evolution using qubitization, and measurement of chemical observables such as reaction yields and rates. Our work gives the first algorithm for quantum simulation of chemistry whose end-to-end complexity achieves sublinear scaling in the size of the grid. We achieve this by developing an exponentially faster method for initial-state-preparation. Photochemistry is a likely early application of our algorithm and we estimate resources required for end-to-end simulations of non-adiabatic dynamics of atmospherically important molecules. Classically intractable photochemical computations could be performed using resources comparable to those required for other chemical applications of quantum computing.