  A quantum memristor is a resistive passive circuit element with memory
engineered in a given quantum platform. It can be represented by a quantum
system coupled to a dissipative environment, in which a system-bath coupling is
mediated through a weak measurement scheme and classical feedback on the
system. In quantum photonics, such a device can be designed from a beam
splitter with tunable reflectivity, which is modified depending on the results
of measurements in one of the outgoing beams. Here, we show that a similar
implementation can be achieved with frequency-entangled optical fields and a
frequency mixer that, working similarly to a beam splitter, produces state
superpositions. We show that the characteristic hysteretic behavior of
memristors can be reproduced when analyzing the response of the system with
respect to the control, for different experimentally-attainable states. Since
memory effects in memristors can be exploited for classical and neuromorphic
computation, the results presented in this work provides the first steps of a
novel route towards constructing quantum neural networks in quantum photonics.
