Helical Logic


Ralph C. Merkle
Xerox PARC
3333 Coyote Hill Road
Palo Alto, CA 94304


K. Eric Drexler
Institute for Molecular Manufacturing
123 Fremont Avenue
Los Altos, CA 94022
This page is the abstract and introduction of Helical Logic. The full paper (about 85 kilobytes) is also available.

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

More information on reversible logic can be found here.


Helical logic is a theoretical proposal for a future computing technology using the presence or absence of individual electrons (or holes) to encode 1s and 0s. The electrons are constrained to move along helical paths, driven by a rotating electric field in which the entire circuit is immersed. The electric field remains roughly orthogonal to the major axis of the helix and confines each charge carrier to a fraction of a turn of a single helical loop, moving it like water in an Archimedean screw. Each loop could in principle hold an independent carrier, permitting high information density. One computationally universal logic operation involves two helices, one of which splits into two "descendant" helices. At the point of divergence, differences in the electrostatic potential resulting from the presence or absence of a carrier in the adjacent helix controls the direction taken by a carrier in the splitting helix. The reverse of this sequence can be used to merge two initially distinct helical paths into a single outgoing helical path without forcing a dissipative transition. Because these operations are both logically and thermodynamically reversible, energy dissipation can be reduced to extremely low levels. This is the first proposal known to the authors that combines thermodynamic reversibility with the use of single charge carriers. It is important to note that this proposal permits a single electron to switch another single electron, and does not require that many electrons be used to switch one electron. The energy dissipated per logic operation can likely be reduced to less than 10^-27 joules at a temperature of 1 Kelvin and a speed of 10 gigahertz, though further analysis is required to confirm this. Irreversible operations, when required, can be easily implemented and should have a dissipation approaching the fundamental limit of ln 2 x kT.


Trends in computer hardware are leading toward higher density and lower energy dissipation. Ultimately, some approaches should result in packing densities in excess of 10^17 logic devices in a cubic centimeter (although the current proposal might require a somewhat larger volume). The trend towards higher packing density strongly influences energy dissipation. Conventional devices must dissipate more than ln(2) x kT joules in switching; so 10^17 conventional devices operating at room temperature (ln(2) x kT~3 x 10^-21 joules for T = 300 Kelvins) at a frequency of 10 gigahertz would dissipate more than 3,000,000 watts; a computer with 1,000 times as many logic elements would still be of reasonable size but would dissipate 3,000,000,000 watts.

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.

This page is part of the nanotechnology web site.