A Cyclic Cooling Algorithm

We introduce a scheme to perform the cooling algorithm, first presented by Oscar Boykin et al. in 2002, for an arbitrary number of times on the same set of qbits. We achieve this goal by adding an additional SWAP-gate and a bath contact to the algorithm. This way one qbit may repeatedly be cooled without adding additional qbits to the system. By using a product Liouville space to model the bath contact we calculate the density matrix of the system after a given number of applications of the algorithm.