  An important aspect that strongly impacts the experimental feasibility of
quantum circuits is the ratio of gate times and typical error time scales.
Algorithms with circuit depths that significantly exceed the error time scales
will result in faulty quantum states and error correction is inevitable. We
present a comparison of the theoretical minimal gate time, i.e., the quantum
speed limit (QSL), for realistic two- and multi-qubit gate implementations in
neutral atoms and superconducting qubits. Subsequent to finding the QSLs for
individual gates by means of optimal control theory we use them to quantify the
circuit QSL of the quantum Fourier transform and the quantum approximate
optimization algorithm. In particular, we analyze these quantum algorithms in
terms of circuit run times and gate counts both in the standard gate model and
the parity mapping. We find that neutral atom and superconducting qubit
platforms show comparable weighted circuit QSLs with respect to the system
size.
