  We design a measurement-based quantum refrigerator with an arbitrary number
of qubits situated in a one-dimensional array that interact through
variable-range XY interactions. The method proposed is based on repeated
evolution followed by a measurement on the single accessible qubit, which has
the potential to reduce the temperature in the rest of the subsystems, thereby
demonstrating cooling in the device. The performance of the refrigerator is
quantified by the fidelity of each local subsystem with the ground state of the
local Hamiltonian and the corresponding probability of success. We identify
system parameters, which include the interaction strength, range of
interactions, initial temperature of each qubit, and the position of the
measured qubit, so that the fidelities of all the unmeasured qubits approach
unity with a nonvanishing probability. We observe that although strong
interactions during evolution are required to achieve cooling, the long-range
interactions typically deteriorate the performance of the refrigerator, which
indicates that interactions are not ubiquitous. We report the scalability and
the saturation property of the success probability with respect to the system
size, which turns out to be independent of the involved system parameters and
the number of repeated measurements. Furthermore, we show that the number of
subsystems which can be cooled changes depending on the odd or even number of
sites in the refrigerator. We argue that the distribution of entanglement
between unmeasured qubits can give a possible explanation of the dependence of
cooling process on the measured and unmeasured sites.
