  Quantum thermodynamics is emerging both as a topic of fundamental research
and as means to understand and potentially improve the performance of quantum
devices. A prominent platform for achieving the necessary manipulation of
quantum states is superconducting circuit quantum electrodynamics (QED). In
this platform, thermalization of a quantum system can be achieved by
interfacing the circuit QED subsystem with a thermal reservoir of appropriate
Hilbert dimensionality. Here we study heat transport through an assembly
consisting of a superconducting qubit capacitively coupled between two
nominally identical coplanar waveguide resonators, each equipped with a heat
reservoir in the form of a normal-metal mesoscopic resistor termination. We
report the observation of tunable photonic heat transport through the
resonator-qubit-resonator assembly, showing that the reservoir-to-reservoir
heat flux depends on the interplay between the qubit-resonator and the
resonator-reservoir couplings, yielding qualitatively dissimilar results in
different coupling regimes. Our quantum heat valve is relevant for the
realisation of quantum heat engines and refrigerators, that can be obtained,
for example, by exploiting the time-domain dynamics and coherence of driven
superconducting qubits. This effort would ultimately bridge the gap between the
fields of quantum information and thermodynamics of mesoscopic systems.
