Global unitary transformations 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 [Fernandez, Lloyd, Mor, Roychowdhury (2004); arXiv: quant-ph/0401135]
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.Comment: 26 pages, 12 + 1 (external) figures; v3: revised manuscrip