Figure 8

Quantum statevector reconstruction by means of \(10^4\) shots (i.e., repeated runs of the simulation with measurement starting with identical initial conditions to determine the n-qubit quantum state) from a one-dimensional simulation on real quantum processors for pure advection (top row) and combined advection and diffusion (bottom row). The quantum simulations have been executed for \(N=2^n\) grid points on \(n=3,4,5\) qubits in the main register. The profile has been transported for \(L/4U\) time units. The target solution (black) is compared against the solutions from a superconducting (IBM Heron, blue) and trapped-ion (IonQ Aria, red) platform. Solid lines are the reconstructed solutions. For the IBM Heron, the shaded area displays the range reaching from the minimum to the maximum deviation in an ensemble of 10 successive production runs. For the IonQ Aria, a single production run was possible only, such that the uncertainty range cannot be plotted. For the ideal statevector simulations, the shaded area corresponds to the range of a standard deviation of \(\pm 3\sigma\).