Real-Time Simulation of Low-Energy Quantum Scattering with Quantum Circuits

Abstract

Simulating chemical dynamics such as atomic and molecular scattering is a natural target for quantum computation, where conventional (classical) hardware faces exponential cost. We present a product-formula quantum algorithm that models single-channel helium–helium scattering by real-time evolution of a Gaussian wavepacket, requiring no precomputation of eigenstates. Interaction with the Lennard-Jones potential and centrifugal barrier is applied unitarily with closed-form circuits, with the evolution processed directly with error-free quantum circuit compilation. Tracking the wave function results in converged phase shifts, from which the deflection function, scattering amplitude, and differential cross section are calculated. Identical-boson integral cross sections agree with time-independent Numerov and log-derivative benchmarks to 6.1%, with a localized residual in s-wave scattering. The construction realizes any potential of the form ∑ i r –m i with the same gate count as a single 1/r term, scales efficiently to multichannel dynamics, and provides a ground-truth operator for benchmarking approximate quantum simulation.