  We theoretically investigate a quantum heat diode based on two interacting
flux qubits coupled to two heat baths. Rectification of heat currents is
achieved by asymmetrically coupling the qubits to the reservoirs modelled as
dissipative $RLC$ resonators. We find that the coherent interaction between the
qubits can be exploited to enhance the rectification factor, which otherwise
would be constrained by the baths temperatures and couplings. Remarkably high
values of rectification ratio up to $\mathcal R \sim 3.5$ can be obtained for
realistic system parameters, with an enhancement up to $\sim 230\%$ compared to
the non-interacting case. The system features the possibility of manipulating
both the rectification amplitude and direction, allowing for an enhancement or
suppression of the heat flow to a chosen bath. For the regime of parameters in
which rectification is maximized, we find a significant increase of the
rectification above a critical interaction value which corresponds to the onset
of a non vanishing entanglement in the system. Finally, we discuss the
dependence of the rectification factor on the bath temperatures and couplings.

Mesoscale and Nanoscale Physics