  We present a collision model for the charging of a quantum battery by
identical nonequilibrium qubit units. When the units are prepared in a mixture
of energy eigenstates, the energy gain in the battery can be described by a
classical random walk, where both average energy and variance grow linearly
with time. Conversely, when the qubits contain quantum coherence, interference
effects buildup in the battery and lead to a faster spreading of the energy
distribution, reminiscent of a quantum random walk. This can be exploited for
faster and more efficient charging of a battery initialized in the ground
state. Specifically, we show that coherent protocols can yield higher charging
power than any possible incoherent strategy, demonstrating a quantum speed-up
at the level of a single battery. Finally, we characterize the amount of
extractable work from the battery through the notion of ergotropy.
