Abstract An algorithm and a system of quantum circuits are developed and applied to compute accurately the S matrix for the transitions between vibrational states of H2 for collisions with H. The algorithm was applied to 100 eV laboratory collision energy at a quantum circuit simulator. The effects of the discretized dissociative continuum to the transition cross sections are carefully studied and accuracy and convergence of the results with the chosen parameters of the algorithm and the collision system are verified by comparison with a solution of the time-dependent Schrodinger equation using the classical algorithm as well as comparison with a few results from the literature.
Abstract An algorithm and a system of quantum circuits are developed and applied to compute accurately the S matrix for the transitions between vibrational states of H2 for collisions with H. The algorithm was applied to 100 eV laboratory collision energy at a quantum circuit simulator. The effects of the discretized dissociative continuum to the transition cross sections are carefully studied and accuracy and convergence of the results with the chosen parameters of the algorithm and the collision system are verified by comparison with a solution of the time-dependent Schrodinger equation using the classical algorithm as well as comparison with a few results from the literature.
The simulation of ion-atom collisions remains a formidable challenge due to the complex interplay between electronic and nuclear degrees of freedom. We present a hybrid quantum-classical computing framework for simulating time-dependent ion-atom collision dynamics, within which two variational quantum time evolution algorithms are implemented. To validate our framework, we simulate the charge-transfer dynamics and compute the corresponding cross sections for the proton-hydrogen collision system across an energy range 1--25 keV. Our results accurately reproduce the charge-transfer dynamics with high fidelity and exhibit very good agreement with available experimental and theoretical cross-section data across the entire energy range. These results highlight the accuracy and applicability of our hybrid quantum-classical framework for scattering cross-section calculations. Our work demonstrates an effective approach for mapping time-dependent many-body collision problems onto near-term quantum computing devices, and also provides promising directions for practical applications of universal quantum computing in the noisy intermediate-scale quantum era.
We propose a hybrid quantum-classical algorithm for solving the time-independent Schrödinger equation for atomic and molecular collisions. The algorithm is based on the S -matrix version of the Kohn variational principle, which computes the fundamental scattering S -matrix by inverting the Hamiltonian matrix expressed in the basis of square-integrable functions. The computational bottleneck of the classical algorithm─symmetric matrix inversion─is addressed here using the variational quantum linear solver (VQLS), a recently developed noisy intermediate-scale quantum (NISQ) algorithm for solving systems of linear equations. We apply our algorithm to single- and multichannel quantum scattering problems, obtaining accurate vibrational relaxation probabilities in collinear atom–molecule collisions. We also show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules. Our results demonstrate that it is possible to calculate scattering cross sections and rates for complex molecular collisions on NISQ quantum processors, opening up the possibility of scalable digital quantum computation of gas-phase bimolecular collisions and reactions of relevance to astrochemistry and ultracold chemistry.
The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.
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
In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical trajectories for the vibration of the hydrogen molecule in several regimes: nearly harmonic, highly anharmonic, and dissociative motion. The results obtained using the D-Wave 2000Q quantum annealer are all consistent and quickly converge to the analytical reference solution. Several alternative strategies for such calculations are explored and it was found that the most accurate results and the best efficiency are obtained by combining the quantum annealer with classical post-processing (greedy algorithm). Importantly, the QDE framework developed here is entirely general and can be applied to solve any system of first-order ordinary nonlinear differential equations using a quantum annealer.
The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here, we present two algorithms that, in conjunction with other methods developed by us, may result in one set of contributions for performing quantum nuclear dynamics in arbitrary dimensions. For one of the two algorithms discussed here, we present a direct map between the Born-Oppenheimer Hamiltonian describing the nuclear wavepacket time evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulates those of the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows. In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits, without using a noise model so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreement with the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density time evolution are in agreement to within a few tenths of a wavenumber.