  We demonstrate the application of the Google Sycamore superconducting qubit
quantum processor to combinatorial optimization problems with the quantum
approximate optimization algorithm (QAOA). Like past QAOA experiments, we study
performance for problems defined on the (planar) connectivity graph of our
hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model
and MaxCut, both high dimensional graph problems for which the QAOA requires
significant compilation. Experimental scans of the QAOA energy landscape show
good agreement with theory across even the largest instances studied (23
qubits) and we are able to perform variational optimization successfully. For
problems defined on our hardware graph we obtain an approximation ratio that is
independent of problem size and observe, for the first time, that performance
increases with circuit depth. For problems requiring compilation, performance
decreases with problem size but still provides an advantage over random
guessing for circuits involving several thousand gates. This behavior
highlights the challenge of using near-term quantum computers to optimize
problems on graphs differing from hardware connectivity. As these graphs are
more representative of real world instances, our results advocate for more
emphasis on such problems in the developing tradition of using the QAOA as a
holistic, device-level benchmark of quantum processors.
