  In this work, we experimentally demonstrate the implementation of a recently
proposed robust and state-independent heat-bath algorithmic cooling (HBAC)
method [1] on an NMR quantum processor. While HBAC methods improve the purity
of a quantum system via iterative unitary entropy compression, they are
difficult to implement experimentally since they use sort operations that are
different for each iteration. The new robust HBAC method proved that optimal
HBAC is possible without prior state information and using a single fixed
operation. We modified the protocol to experimentally perform efficient cooling
of 13C and 15N spins and provide an optimal decomposition of this modified
protocol in terms of quantum gates. This is the first time that optimal HBAC
has been experimentally demonstrated on 15N spins. We examined the relaxation
dynamics of these algorithmically cooled spins, in order to ascertain the
effect of decoherence on the cooled states.
