ing to a VN program, as decomposed into a series of micro-instructions and bit processing through such complex logic networks. We shall now move on to the core of the issue: the reversibility of computing and the need to find alternative ways to process information. As we have learnt, the above description constitutes a basic inventory of classical logic gates and circuit networks, which (except for NOT gate) we know perform nonreversible operations. According to Landauer's principle, which was described earlier, the infor- mation erasure of each input bit corresponds to a minimum heat and entropy generation of Q = k T log 2 and H = kB log 2, respectively. The power consumption of the logic gates and of the various electronic circuits (including digital amplifiers to compensate for signal propagation or splitting loss) also represents a source of heat and entropy, whose measures are orders of magnitude greater than Landauer's bound. The heat dis- sipation is estimated to be Q' = 500k T log 2 = 500Q for elementary logic gates, and Q" = 108 kT 2 108 Q for the CPU in ordinary home computers. 13 Most of this heat, of resistive origin, could be alleviated if computers would be run at ultra-low tempera- tures (T 0), using "superconducting" electronics. If such a computer could ever be built, then one would reach the ultimate limits predicted by Landauer's bound. The key question, then, is whether or not it is possible to build computers with reversible logic. As previously hinted, physicists, who are attached to the concept of reversible processes, intuitively suspect that it should be possible to manipulate information in a reversible 12 See: http://tams-www.informatik.uni-hamburg.de/applets/hades/webdemos/20-arithmetic/50-74181/ demo-74181-ALU.html. 13 See (respectively): M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press, 2000) and V. Vedral and M.B. Plenio, Basics of quantum computation. Prog. Quant. Electron., 22 (1998), 1-39. 15.3 Reversible logic gate