Quantum Simulation of Variable-Speed Multidimensional Wave Equations via Clifford-Assisted Pauli Decomposition

The simulation of multidimensional wave propagation with variable material parameters is a computationally intensive task, with applications from seismology to electromagnetics. While quantum computers offer a promising path forward, their algorithms are often analyzed in the abstract oracle model, which can mask the high gate-level complexity of implementing those oracles. We present a framework for constructing a quantum algorithm for the multidimensional wave equation with a variable speed profile. The core of our method is a decomposition of the system Hamiltonian into sets of mutually commuting Pauli strings, paired with a dedicated diagonalization procedure that uses Clifford gates to minimize simulation cost. Within this framework, we derive explicit bounds on the number of quantum gates required for Trotter–Suzuki-based simulation. Our analysis reveals significant computational savings for structured block-model speed profiles compared to general cases. Numerical experiments in three dimensions confirm the practical viability and performance of our approach. Beyond providing a concrete, gate-level algorithm for an important class of wave problems, the techniques introduced here for Hamiltonian decomposition and diagonalization enrich the general toolbox of quantum simulation.