Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!aramis.rutgers.edu!athos.rutgers.edu!nanotech From: merkle.pa@xerox.com Newsgroups: sci.nanotech Subject: Re: Message-ID: Date: 28 Jun 89 21:05:05 GMT Sender: nanotech@athos.rutgers.edu Lines: 63 Approved: nanotech@aramis.rutgers.edu In article <8906270612.AA12977@athos.rutgers.edu> landman@sun.com (Howard A. Landman) writes: >We'll probably >hit the kT limit first, even with cryonic circuits (liquid nitrogen >is still awfully hot). There is no kT limit. See "The fundamental physical limits of computation" by Charles H. Bennet and Rolf Landauer, Scientific American Vol. 253, July 1985, pages 48-56. Computational devices that dissipate less than kT energy per gate operation have already been designed, though none has yet been built. Logically reversible gates need not, in principle, dissipate any fixed amount of energy per operation. Only irreversible gates must dissipate kT energy per operation. The Fredkin gate is the classic example of a reversible gate. It has three inputs, and three outputs. The truth table for a Fredkin gate is: I1 I2 I3 O1 O2 O3 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 A Fredkin gate can be described by a computer program as: O1 = I1; IF I1 == 0 THEN O2 = I2; O3 = I3 END IF; IF I1 == 1 THEN O2 = I3; O3 = I2 END IF; The input state can be deduced from the output state, hence the gate is "reversible." Energy dissipation by such a gate can be arbitrarily small. In principle, therefore, we can achieve an arbitrarily large number of gate operations for each watt of energy expended. In practice, we can expect to achieve at least 10**24 gate operations per watt, because Likharev proposed a reversible gate which dissipates 10**-24 joules per operation at 4 degrees Kelvin when operating at 10**9 operations per second ("Classical and Quantum Limitations on Energy Consumption in Computation" by K. K. Likharev, International Journal of Theoretical Physics, Vol. 21, Nos. 3/4, 1982). How many more gate operations we can achieve per watt is at present unclear. It is probable that we can achieve a great deal more (many orders of magnitude improvement). [I am not convinced that a useful computer can be built of Fredkin or other reversible logic. The reason is that the "trick" depends on not destroying information. Maxwell's demon uses energy (entropy really, but it takes "useful work" ie energy, to destroy entropy) not in finding a molecule, but in forgetting it to get ready for the next one. Let me put it another way: to build a Fredkin gate machine, you must connect *all* of the outputs to something--no dangling wires. To make something useful you wind up in effect continuously writing the state of the machine out into memory. And you can't clear the memory to start over, or you use up all the energy you saved by using Fredkin gates in the first place. --JoSH]