  Global unitary transformations (OPTSWAPS) that optimally increase the bias of
any mixed computation qubit in a quantum system -- represented by a diagonal
density matrix -- towards a particular state of the computational basis which,
in effect, increases its purity are presented. Quantum circuits that achieve
this by implementing the above data compression technique -- a generalization
of the 3B-Comp used before -- are described. These circuits enable purity
increment in the computation qubit by maximally transferring part of its von
Neumann or Shannon entropy to any number of surrounding qubits and are valid
for the complete range of initial biases. Using the optswaps, a practicable new
method that algorithmically achieves hierarchy-dependent cooling of qubits to
their respective limits in an engineered quantum register opened to the
heat-bath is delineated. In addition to multi-qubit purification and satisfying
two of DiVincenzo's criteria for quantum computation in some architectures, the
implications of this work for quantum data compression and quantum
thermodynamics are discussed.
