Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor

Abhishek Shringi; Hsuan-Cheng Wu; Ahmed Shokry; Xiantao Li; Mahmut Taylan Kandemir

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arXiv · 2607.28499

Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor

Abhishek Shringi·Hsuan-Cheng Wu·Ahmed Shokry·Xiantao Li·Mahmut Taylan Kandemir

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Abstract

Wave equations provide a natural testbed for near-term quantum simulation of partial differential equations, but hardware demonstrations have remained limited in spatial dimension, equation class, system size, and physically meaningful output. We develop and benchmark structure-preserving, Fourier-based quantum circuits for the one- and two dimensional acoustic wave equations and Dirac dynamics with variable mass on the Quantinuum H2-2 trapped-ion processor. The experiments include one-dimensional grids with up to $1024$ points and $32\times32$ two-dimensional grids, corresponding to an encoded state-space dimension of up to $4096$. Rather than reconstructing the full fields, we estimate subdomain kinetic energies directly from measurement samples. Across all tested acoustic and Dirac dynamics problems, the H2-2 results track the classical kinetic-energy dynamics with mean absolute errors between $5.9\times10^{-3}$ and $2.4\times10^{-2}$. At fixed retained bandwidth, the compiled gate counts grow approximately quadratically with the number of grid qubits; the acoustic circuit sizes are essentially independent of evolution time, whereas the cost also grows with the number of product-formula steps. These results provide hardware-level evidence that accurate observable dynamics can remain resolvable for structured wave problems with thousands of encoded degrees of freedom on a present-day trapped-ion processor.

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Abhishek Shringi, Hsuan-Cheng Wu, Ahmed Shokry, Xiantao Li, Mahmut Taylan Kandemir. 2026-07-30. Structure-Preserving Quantum Simulation of Wave Equations on a Trapped-Ion Processor. https://arxiv.org/abs/2607.28499

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