Ralph C. Merkle Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304 merkle@xerox.com and K. Eric Drexler Institute for Molecular Manufacturing 123 Fremont Avenue Los Altos, CA 94022This page is the abstract and introduction of

This article has been published in
*Nanotechnology* (1996) **7** pages 325-339.

More information on reversible logic can be found
*here*.

Conventional circuits perform more poorly. Even an idealized device which used a one volt power supply and dissipatively discharged a single electron to ground during a switching operation would dissipate one electron volt per switching operation. At T=300 Kelvins, this is 40 x kT per switching operation or about 160,000,000 watts for a computer with 10^17 logic elements operating at 10 gigahertz. If each switching operation involves hundreds of electrons then energy dissipation enters the multigigawatt range.

New thermodynamically reversible circuits (including CMOS, nMOS and CCD-based logic circuits) would fare better, but these circuits still have dissipative losses caused by the resistance of the circuit. While resistance in sufficiently small wires can be very low, if such wires are connected to each other, to logic elements or to larger structures it is common to find resistances of the order of 13,000 ohms (half of h/e^2, where h is Planck's constant) (note that no claim is made that the successful operation of such circuits must fundamentally require resistances of this magnitude, we simply note that shrinking current circuits to a small scale would result in such resistances: further research in this area might be successful in dealing with this problem). Assuming that 100 electrons were required to charge and discharge the wires and capacitive loads in each logic element, and assuming a resistance of approximately 13,000 ohms, we would still find our 10^17 gate computer dissipating tens of megawatts even using these particular thermodynamically reversible methods.

If the exponential trends of recent decades continue, energy dissipation per logic operation will reach kT (for T=300 Kelvins) early in the next century. Either energy dissipation per logic operation will be reduced significantly below 3 x 10^-21 joules, or we will fail to achieve computers that simultaneously combine high packing densities with gigahertz or higher speeds of operation. There are only two ways that energy dissipation can be reduced below 3 x 10^-21 joules: by operating at temperatures below room temperature (thus reducing kT), or by using thermodynamically reversible logic. Low temperature operation doesn't actually reduce total energy dissipation, it just shifts it from computation to refrigeration. Thermodynamically reversible logic elements, in contrast, can reduce total energy dissipation per logic operation to well below kT. This paper analyzes a proposed thermodynamically reversible single electron logic system. To achieve high reliabilit while switching single electrons, we analyze operation at ~1 Kelvin.

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