  In this work, we solve the quantum absorption refrigerator analytically in
the space of holomorphic functions with Gaussian measure . Our approach
simplifies the calculations since for a given quantum system the coordinate
representation of any quantum state is always more complicated than its
corresponding expression written with respect to the phase-space coordinate
$z_{i}$. We finally discuss the computational complexity of the holomorphic
representation and compare it with the computational complexity of the standard
operator method and prove the efficiency of the holomorphic representation in
computing some tasks. Our treatment is applicable to all quantum heat engines
and refrigerators.
