Re: Reversible Computers

Michael Nielsen (
Sat, 27 Jun 1998 12:27:39 -0600 (MDT)

On Sat, 27 Jun 1998, John K Clark wrote:

> On Thu, 25 Jun 1998 Michael Nielsen <> Wrote:
> >The reversible architectures I am aware of have higher fundamental
> >error rates than existing irreversible architectures, and will
> >likely require considerable error correction. Error correction, in
> >turn, involves the dissipation of heat, by elementary thermodynamic
> >arguments. Essentially, error correction is a procedure for
> >lowering the entropy of a physical system (the computer). The
> >entropic cost is paid in heat dissipated into the environment.
> There may be engineering reasons that with current technology reversible
> computers would make more errors than the irreversible type, but I don't see
> any fundamental physical reason why that should be so.

The usual hand-waving argument is that using larger systems as basic logical
elements automatically gives some of the redundancy that is the basis for
error correction; smaller systems lack this redundancy, and are
therefore more subject to error. It's simply a problem of the size of
the potentials involved -- if there is a large potential barrier between
the two logical states, then they are resilient against fluctuations; if
not, then they become error prone, due to thermal and quantum
fluctuations. In specific instances this can actually be made into
a pretty solid argument, but in general, I doubt it. So far as I am
aware, it is certainly empirically true for all known systems. Our solid
state computing devices have error rates in the 10^{-18} range, while
single particle systems are lucky to get down to 10^{-2}.

Suppose we want to perform 10^{12} operations on 10^{12} bits -- not
unreasonable, if we want to go beyond the 2020 Moore's Law. Then we will
need single particle systems with error rates of 10^{-24}, if we are to
avoid the need for error correction, and therefore heat dissipation.

> Landauer, Bennett and Merkle have shown that with reversible computing the
> amount of energy needed to make a calculation can be made arbitrarily small,
> by slowing down the calculation a little.

Could you please send me a reference to Merkle's work on this?

Michael Nielsen