  Today's quantum processors composed of fifty or more qubits have allowed us
to enter a computational era where the output results are not easily
simulatable on the world's biggest supercomputers. What we have not seen yet,
however, is whether or not such quantum complexity can be ever useful for any
practical applications. A fundamental question behind this lies in the
non-trivial relation between the complexity and its computational power. If we
find a clue for how and what quantum complexity could boost the computational
power, we might be able to directly utilize the quantum complexity to design
quantum computation even with the presence of noise and errors. In this work we
introduce a new reservoir computational model for pattern recognition showing a
quantum advantage utilizing scale-free networks. This new scheme allows us to
utilize the complexity inherent in the scale-free networks, meaning we do not
require programing nor optimization of the quantum layer even for other
computational tasks. The simplicity in our approach illustrates the
computational power in quantum complexity as well as provide new applications
for such processors.
