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

Area of Science:

• Quantum Chemistry
• Computational Physics
• Chemical Physics

Background:

• Solving the time-independent Schrödinger equation is crucial for understanding atomic and molecular collisions.
• Classical computational methods face bottlenecks, particularly in symmetric matrix inversion for scattering calculations.

Purpose of the Study:

• To develop a hybrid quantum-classical algorithm for accurate solutions to the Schrödinger equation in atomic and molecular collisions.
• To address the computational bottleneck of symmetric matrix inversion in scattering calculations using quantum computing.

Main Methods:

• The algorithm employs the S-matrix version of the Kohn variational principle.
• It utilizes the variational quantum linear solver (VQLS), a noisy intermediate-scale quantum (NISQ) algorithm, to solve linear equations.
• The method involves inverting the Hamiltonian matrix within a basis of square-integrable functions.

Main Results:

• Accurate vibrational relaxation probabilities were obtained for collinear atom-molecule collisions.
• The algorithm successfully applied to single- and multichannel quantum scattering problems.
• Demonstrated scalability for simulating collisions of large polyatomic molecules.

Conclusions:

• Hybrid quantum-classical approaches can accurately compute scattering cross sections and rates for complex molecular collisions.
• Noisy intermediate-scale quantum (NISQ) processors show potential for digital quantum computation of bimolecular collisions.
• This opens possibilities for simulating reactions relevant to astrochemistry and ultracold chemistry.