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Real-Time Simulation of Low-Energy Quantum Scattering with Quantum Circuits
Joshua M Courtney1, Phillip C Stancil2
1Department of Physics and Astronomy and the Center for Simulational Physics, University of Georgia, Athens, Georgia30602, United States.
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 ∑ir-mi 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.
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