Uncertainty principle and minimal energy dissipation in the computer

Abstract

Reversible computation is briefly reviewed, utilizing a refined version of the Bennett-Fredkin-Turing machine, invoked in an earlier paper. A dissipationless classical version of this machine, which has no internal frietion, and where the computational velocity is determined by the initial kinetic energy, is also described. Such a machine requires perfect parts and also requires the unrealisstic assumption that the many extraneous degrees of freedom, which contribute to the physical structure, do not couple to the information-bearing degrees of freedom, and thus cause no friction Quantum mechanical computation is discussed at two levels. First of all we deplore the assertion. repcatedly found in the literature, that the uncertainty principle. ΔEΔt≈h, with Δt equated to a switching time, yields any information about energydissipation. Similarly we point out that computation is not an iterated transmission and receiving process, and that considerations, which avoid the uncertainty principle, and instead use quantum mechanical channel capacity considerations, are equally unfounded. At a more constructive level we ask whether there is a quantum mechanical version of the dissipationless computer. Benioff has proposed one possible answer Quantum mechanical versions of dissipationless computers may suffer from the problems found in electron transport in disordered one-dimensional periodic potentials. The buildup of internal reflections may give a transmission coefficient. through the whole computation, which decreases exponentially with the length of the computation.