Physical regimes of quartic quantum advantage in elastic media simulation
Abstract
Quantum algorithms for elastic media simulation have been conjectured to offer up to a quartic quantum advantage over classical methods; however, the devil is always in the details. Here, we determine key physical conditions under which this quartic separation could be achieved in the relevant parameters. For continuum elastic dynamics at fixed volume with spatial convergence order m, we find that the end-to-end speedup is of order (m+4)/(m+1) in the simulation time, and 4/(m+1) in the accuracy, with exponential memory advantage. For elastic lattice systems, we define microscopically resolved bulk observables (MRBOs) as those that can be efficiently extracted from a quantum state, but cannot be resolved by a known continuum model with fewer degrees of freedom than the lattice. We then argue that the estimation of MRBOs is a candidate problem for quartic quantum advantage in problem size. We propose MRBOs for pseudorandom heterogeneous materials as an explicit end-to-end application where this occurs, while admitting efficient `quantum cheese' encodings of the material properties. We thus demonstrate how the interplay between regularity, physical scale, observable sensitivity and quantum encodability constrains the relation between classical and quantum complexity.
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BibTeX
@misc{jennings2026physical,
title = {{Physical regimes of quartic quantum advantage in elastic media simulation}},
author = {David Jennings and Kamil Korzekwa and Matteo Lostaglio and Tamás Vaszary},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06975},
eprint = {2611.06975},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06975},
}
RIS
TY - UNPB
TI - Physical regimes of quartic quantum advantage in elastic media simulation
AU - David Jennings
AU - Kamil Korzekwa
AU - Matteo Lostaglio
AU - Tamás Vaszary
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06975
UR - https://arxiv.org/abs/2611.06975
AB - Quantum algorithms for elastic media simulation have been conjectured to offer up to a quartic quantum advantage over classical methods; however, the devil is always in the details. Here, we determine key physical conditions under which this quartic separation could be achieved in the relevant parameters. For continuum elastic dynamics at fixed volume with spatial convergence order m, we find that the end-to-end speedup is of order (m+4)/(m+1) in the simulation time, and 4/(m+1) in the accuracy, with exponential memory advantage. For elastic lattice systems, we define microscopically resolved bulk observables (MRBOs) as those that can be efficiently extracted from a quantum state, but cannot be resolved by a known continuum model with fewer degrees of freedom than the lattice. We then argue that the estimation of MRBOs is a candidate problem for quartic quantum advantage in problem size. We propose MRBOs for pseudorandom heterogeneous materials as an explicit end-to-end application where this occurs, while admitting efficient `quantum cheese' encodings of the material properties. We thus demonstrate how the interplay between regularity, physical scale, observable sensitivity and quantum encodability constrains the relation between classical and quantum complexity.
ER -