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

Tunable Non-Markovianity for Bosonic Quantum Memristors