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arXiv:2304.06089 · The Journal of Physical Chemistry Letters

A Hybrid Quantum-Classical Algorithm for Multichannel Quantum Scattering of Atoms and Molecules

Xiaodong Xing, Alejandro Gomez Cadavid, Artur F. Izmaylov, Timur V. Tscherbul

Published Jun 30, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1021/acs.jpclett.3c00985

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All elements of a quantum algorithm for calculations of rotationally inelastic molecule + atom scattering within the framework of a mixed quantum/classical theory are outlined. In this approach, the rotational motion of the molecule is described quantum mechanically using the time-dependent Schrödinger equation, while the scattering process of two collision partners is treated classically. The matrix of potential coupling is precomputed on a classical processor, whereas the quantum hardware is used to propagate the system of coupled equations for the rotational state-to-state transitions. All quantum circuits needed for practical implementation of the algorithm are presented. First, the quantum codes written in Qiskit are rigorously tested by running calculations for a N 2 + O collision on a classical emulator of quantum hardware using a realistic potential energy surface of this system and comparing these results against the results obtained by the MQCT code. Next, these codes are run on the actual quantum hardware, such as the publicly available IBM Brisbane, Kyiv, and Sherbrooke . A very good agreement with benchmark data was obtained. To the best of our knowledge, this is the first proof-of-principle calculation of inelastic scattering implemented successfully on a quantum computer using a case study within mixed quantum/classical framework.
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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.