  Memristive systems are generalisations of memristors, which are resistors
with memory. In this paper, we present a quantum description of memristive
systems. Using this model we propose and experimentally demonstrate a simple
and practical scheme for realising memristive systems with quantum dots. The
approach harnesses a phenomenon that is commonly seen as a bane of
nanoelectronics, i.e. switching of a trapped charge in the vicinity of the
device. We show that quantum-dot memristive systems have hysteresis
current-voltage characteristics and quantum jump induced stochastic behaviour.
Realising such a quantum memristor completes the menu of components for quantum
circuit design.
