A quantum algorithm for computing dispersal of submarine volcanic tephra

In this paper, we develop a quantum computing algorithm for solving the partial differential equation (PDE) for tephra dispersal through advection in the semi-infinite horizontal buoyant region of a submarine volcanic eruption. The concentration of pyroclastic particles in the fluid domain of a hydrothermal megaplume provides important information about the rate of volcanic energy release, mechanism of formation of the megaplume, and submarine depositional patterns. This work leveraging on previous works [F. Gaitan, NPJ Quantum Inf. 6, 61 (2020); F. Gaitan, Adv. Quantum Tech. 4, 2100055 (2021)] further opens up opportunities to solve wider classes of PDEs with different applications of interest. Some additional specific contributions of this work are transforming the semi-infinite spatial domain problem into a problem on a finite spatial domain for applying the quantum algorithm, and the investigation into the effect of spatial and temporal resolution on the solution of PDEs for the quantum algorithm. Furthermore, possible modification of the algorithm with different spatial discretization schemes has been presented and their influence and implications on the solution of the PDE have been discussed. Also, studies are conducted to examine the effect of regularity conditions in time and the presence of statistical noise in the spatial domain, on the solutions obtained using quantum algorithms. The study in this paper paves an important pathway to venture into other types of advection-diffusion problems.