  Resistive-switching memories are alternative to Si-based ones, which face
scaling and high power consumption issues. Tetrahedral amorphous carbon (ta-C)
shows reversible, non-volatile resistive switching. Here we report polarity
independent ta-C resistive memory devices with graphene-based electrodes. Our
devices show ON/OFF resistance ratios$\sim$4x$10^5$, ten times higher than with
metal electrodes, with no increase in switching power, and low power
density$\sim$14$\mu$W/$\mu$m$^2$. We attribute this to a suppressed tunneling
current due to the low density of states of graphene near the Dirac point,
consistent with the current-voltage characteristics derived from a quantum
point contact model. Our devices also have multiple resistive states. This
allows storing more than one bit per cell. This can be exploited in a range of
signal processing/computing-type operations, such as implementing logic,
providing synaptic and neuron-like mimics, and performing analogue signal
processing in non-von-Neumann architectures
