  We study large-scale applications using a GPU-accelerated version of the
massively parallel J\"ulich universal quantum computer simulator (JUQCS--G).
First, we benchmark JUWELS Booster, a GPU cluster with 3744 NVIDIA A100 Tensor
Core GPUs. Then, we use JUQCS--G to study the relation between quantum
annealing (QA) and the quantum approximate optimization algorithm (QAOA). We
find that a very coarsely discretized version of QA, termed approximate quantum
annealing (AQA), performs surprisingly well in comparison to the QAOA. It can
either be used to initialize the QAOA, or to avoid the costly optimization
procedure altogether. Furthermore, we study the scaling of the success
probability when using AQA for problems with 30 to 40 qubits. We find that the
case with the largest discretization error scales most favorably, surpassing
the best result obtained from the QAOA.
