  We study the tunable control of the non-Markovianity of a bosonic mode due to
its coupling 1 to a set of auxiliary qubits, both embedded in a thermal
reservoir. Specifically, we consider a cavity 2 mode coupled to auxiliary
qubits described by the Tavis-Cummings model. As a figure of merit, 3 we define
the dynamical non-Markovianity as the tendency of a system to return to its
initial state, 4 instead of evolving monotonically to its steady state. We
study how this dynamical non-Markovianity 5 can be manipulated in terms of the
qubit frequency. We find that the control of the auxiliary systems 6 affects
the cavity dynamics as an effective time-dependent decay rate. Finally, we show
how this 7 tunable time-dependent decay rate can be tuned to engineer bosonic
quantum memristors, involving 8 memory effects that are fundamental for
developing neuromorphic quantum technologies.
