The human brain has inspired novel concepts complementary to classical and quantum computing architectures, such as artificial neural networks and neuromorphic computers, but it is not clear how their performances compare. Here we report a new methodological framework for benchmarking cognitive performance based on solving computational problems with increasing problem size. We determine computational efficiencies in experiments with human participants and benchmark these against complexity classes. We show that a neuromorphic architecture with limited field-of-view size and added noise provides a good approximation to our results. The benchmarking also suggests there is no quantum advantage on the scales of human capability compared to the neuromorphic model. Thus, the framework offers unique insights into the computational efficiency of the brain by considering it a black box.