  Quantum state transfer from an information-carrying qubit to a receiving
qubit is ubiquitous for quantum information technology. In a closed quantum
system, this task requires precisely-timed control of coherent qubit-qubit
interactions that are intrinsically reciprocal. Here, breaking reciprocity by
tailoring dissipation in an open system, we show that it is possible to
autonomously transfer a quantum state between stationary qubits without
time-dependent control. We present the general requirements for this
directional transfer process, and show that the minimum system dimension for
transferring one qubit of information is 3 $\times$ 2 (between one physical
qutrit and one physical qubit), plus one auxiliary reservoir. We propose
realistic implementations in present-day superconducting circuit QED
experiments, and further propose schemes compatible with long-distance state
transfer using impedance-matched dissipation engineering.
