Physical regimes of quartic quantum advantage in elastic media simulation

arXiv:2611.06975v1 Announce Type: new 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.