Digital quantum simulation offers a promising route for studying quantum dynamics, but efficient operator representations and circuit depth remain key challenges for near-term hardware. We investigate one-dimensional wave packet dynamics using a grid-based encoding of the wave function onto qubit registers. Time evolution is implemented via split-operator approach, with kinetic energy operator applied using Quantum Fourier Transform (QFT) with polynomial scaling and potential energy operator expressed through commuting Pauli-Z gates, improving accuracy and enabling incorporation of arbitrary discretized potentials. While the full Pauli decomposition of Hamiltonian scales exponentially as O(4^n ), the present approach reduces the operator scaling to O(2^n) for n qubits. We benchmark this approach on classical simulators and quantum hardware (IBM Quantum and IonQ) for two- to five-qubit implementations. For two- and three-qubit cases, all platforms qualitatively reproduce the benchmarked dynamics; at larger qubit counts, the IBM results deviate more strongly, whereas IonQ remains closer to the benchmark.
@article{arxiv.2605.20078,
title = {On Performance and Limitations of NISQ Hardware for Simulations of Quantum Wave Packet Dynamics},
author = {Tamila Kuanysheva and Jonathan Andrade-Plascencia and Jayakrushna Sahoo and Brian Kendrick and Dmitri Babikov},
journal= {arXiv preprint arXiv:2605.20078},
year = {2026}
}