The Chance of Error in Atomic Sized Computers

The first thing that you would worry about when things get very small is Brownian motion--everything is shaking about and nothing stays in place. How can you control the circuits then? Furthermore, if a circuit does work, doesn't it now have a chance of accidentally jumping back? If we use two volts for the energy of this electric system, which is what we ordinarily use, that is eighty times the thermal energy at room temperature (kT=1/40 volt) and the chance that something jumps backward against 80 times thermal energy is e, the base of the natural logarithm, to the power minus eighty, or 10^-43. What does that mean? If we had a billion transistors in a computer (which we don't yet have), all of them switching 10^10 times a second (a switching time of a tenth of a nanosecond), switching perpetually, operating for 10^9 seconds, which is 30 years, the total number of switching operations in such a machine is 10^28. The chance of one of the transistors going backward is only 10^-43, so there will be no error produced by thermal oscillations whatsoever in 30 years. If you don't like that, use 2.5 volts and then the probability gets even smaller. Long before that, real failures will come when a cosmic ray accidentally goes through the transistor, and we don't have to be more perfect than that.


As things get very small we have to worry about brownian motion and quantum effects on the system.

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 Computing Machines of the Future
Books, Brochures, and Chapters>Book Chapter:  Feynman, Richard (1985), Computing Machines of the Future, Nishina Memorial Foundation, Nishina Memorial Lecture, Retrieved on 2010-11-07