  We present a quantum heat switch based on coupled superconducting qubits,
connected to two $LC$ resonators that are terminated by resistors providing two
heat baths. To describe the system we use a standard second order master
equation with respect to coupling to the baths. We find that this system can
act as an efficient heat switch controlled by the applied magnetic flux. The
flux influences the energy level separations of the system, and under some
conditions, the finite coupling of the qubits enhances the transmitted power
between the two baths, by an order of magnitude under realistic conditions. At
the same time, the bandwidth at maximum power of the switch formed of the
coupled qubits is narrowed.
