On Performance and Limitations of NISQ Hardware for Simulations of Quantum Wave Packet Dynamics

TL;DR

This paper explores the capabilities and limitations of NISQ quantum hardware for simulating quantum wave packet dynamics, proposing an efficient encoding and implementation method tested on real quantum devices.

Contribution

It introduces a grid-based encoding and split-operator approach that reduces operator scaling and is tested on IBM and IonQ hardware for small qubit systems.

Findings

All platforms qualitatively reproduce dynamics for 2-3 qubits.

IonQ hardware performs closer to benchmarks at larger qubit counts.

IBM hardware shows more deviation as qubit number increases.

Abstract

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.