Fractal fidelity as a signature of quantum chaos

We analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations if and only if the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the case of integrable dynamics, the appearance of fidelity fractal fluctuations is a signal of a highly corrupted simulation. We conjecture that fidelity fractal fluctuations are a signature of the appearance of quantum chaos. Our analysis can be realized already by a few-qubit quantum processor.