Quantum approximate optimization of non-planar graph problems on a planar superconducting processor

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