  Algorithmic cooling is a potentially important technique for making scalable
NMR quantum computation feasible in practice. Given the constraints imposed by
this approach to quantum computing, the most likely cooling algorithms to be
practicable are those based on simple reversible polarization compression (RPC)
operations acting locally on small numbers of bits. Several different
algorithms using 2- and 3-bit RPC operations have appeared in the literature,
and these are the algorithms I consider in this note. Specifically, I show that
the RPC operation used in all these algorithms is essentially a majority vote
of 3 bits, and prove the optimality of the best such algorithm. I go on to
derive some theoretical bounds on the performance of these algorithms under
some specific assumptions about errors.
