Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to discrete optimization problems with the quantum approximate optimization algorithm (QAOA). We execute the QAOA across a variety of problem sizes and circuit depths for random instances of the Sherrington-Kirkpatrick model and 3-regular MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. We also study the Ising model restricted to the planar graph of our hardware. Exhaustive search of QAOA parameters shows theoretical agreement even across the largest instances studied (23 qubits) and variational optimization on these landscapes is successful. For Ising models on the hardware graph we obtain an approximation ratio that is independent of problem size and observe that performance increases with circuit depth up to three or four layers of the algorithm. For the problems requiring compilation, we show that performance decreases with problem size but still provides an advantage over random guessing for problems on fewer than 18 qubits. Our experiment highlights the challenges of using quantum computers to optimize high dimensional graph problems and contributes to the developing tradition of using the QAOA as a holistic, device-level benchmark of performance on a popular quantum algorithm applied to well-studied optimization problems.