  Harnessing the quantum computation power of the present
noisy-intermediate-size-quantum devices has received tremendous interest in the
last few years. Here we study the learning power of a one-dimensional
long-range randomly-coupled quantum spin chain, within the framework of
reservoir computing. In time sequence learning tasks, we find the system in the
quantum many-body localized (MBL) phase holds long-term memory, which can be
attributed to the emergent local integrals of motion. On the other hand, MBL
phase does not provide sufficient nonlinearity in learning highly-nonlinear
time sequences, which we show in a parity check task. This is reversed in the
quantum ergodic phase, which provides sufficient nonlinearity but compromises
memory capacity. In a complex learning task of Mackey-Glass prediction that
requires both sufficient memory capacity and nonlinearity, we find optimal
learning performance near the MBL-to-ergodic transition. This leads to a
guiding principle of quantum reservoir engineering at the edge of quantum
ergodicity reaching optimal learning power for generic complex reservoir
learning tasks. Our theoretical finding can be readily tested with present
experiments.
