  We design and implement quantum circuits for the simulation of the
one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The
circuit depth of our approach scales as $O(n^{2})$ for $n$ qubits representing
the solution on $2^n$ grid points, and leads to infidelities of $O(2^{-4n}
t^{2})$ for simulation time $t$ assuming smooth initial conditions. By varying
the qubit count we study the interplay between the algorithmic and physical
gate errors to identify the optimal working point of minimum total error. Our
approach to simulating the wave equation can readily be adapted to other
quantum processors and serve as an application-oriented benchmark.
