  We propose to use a few-qubit system as a compact quantum refrigerator for
cooling an interacting multi-qubit system. We specifically consider a central
qubit coupled to $N$ ancilla qubits in a so-called spin-star model as our
quantum refrigerator. We first show that if the interaction between the qubits
is of the longitudinal and ferromagnetic Ising model form, the central qubit is
colder than the environment. The colder central qubit is then proposed to be
used as the refrigerant interface of the quantum refrigerator to cool down
general quantum many-qubit systems. We discuss a simple refrigeration cycle,
considering the operation cost and cooling efficiency, which can be controlled
by $N$ and the qubit-qubit interaction strength. Besides, bounds on the
achievable temperature are established. Such few-qubit compact quantum
refrigerators can be significant to reduce dimensions of quantum technology
applications, can be easy to integrate into all-qubit systems, and can increase
the speed and power of quantum computing and thermal devices.
