What can 10 qubits do to solve classification problems?*

In the last few years, the size of quantum processors has increased roughly by an order of magnitude in terms of the number of qubits.  This rapid growth has encouraged significant efforts to find suitable applications for these noise quantum processors.  So far, however, the accumulated evidence shows its difficulties, and it seems that it is not so easy to extract the practical computational power out of these devices, which are otherwise capable to create complex dynamics.  In this talk, we present a new approach to use such complex quantum dynamics for a practical computational task.  As a concrete example, we show a computational model based on quantum neural networks referred as quantum extreme reservoir computation (QERC).  The performance of this model is evaluated by solving classification problems and a comparison to the classical approach with a similar resource. 

This model was initially designed using the network structure virtually imbedded on the Hilbert space.  To investigate the relation of the computational power as the QERC and the network property of the unitary map on the Hilbert space, we analyze the unitary map created by the quantum reservoir dynamics and show a certain property can help the performance on solving these classification problems.