Quantum Thermodynamics applied for Quantum Refrigerators cooling down a qubit

We discuss a quantum refrigerator to increase the ground state probability of a target qubit whose energy difference between the ground and excited states is less than the thermal energy of the environment. We consider two types of quantum refrigerators: (1) one extra qubit with frequent pulse operations and (2) two extra qubits without them. These two types of refrigerators are evaluated from the viewpoint of quantum thermodynamics. More specifically, we calculate the heat removed from the target qubit, the work done for the system, and the coefficient of performance (COP), the ratio between the heat ant the work. We show that the COP of the second type outperforms that of the first type. Our results are useful to design a high-performance quantum refrigerator cooling down a qubit.