*(Also known as Charge Recovery Logic or Adiabatic Logic)*

As we pack more and more logic elements into smaller and smaller volumes and clock them at higher and higher frequencies, we dissipate more and more heat. This creates at least three problems:

- Energy costs money.
- Portable systems exhaust their batteries.
- Systems overheat.

Today's computers erase a bit of information (in the sense
used here) every time they perform a logic operation.
These logic operations are therefore called "irreversible."
This erasure is done very inefficiently, and much more
than *kT* is dissipated for each bit erased.

If we are to continue the revolution in computer hardware performance
we must continue to reduce the energy dissipated by each
logic operation. Today, because we are dissipating much more
than *kT*, we can do this by improving conventional
methods, i.e., by improving the efficiency with which we
erase information.

An alternative is to use logic operations that do not erase
information. These are called *reversible* logic
operations, and in principle they can dissipate arbitrarily
little heat. As the energy dissipated per
irreversible logic operation approaches the fundamental limit
of ln 2 x *kT*, the use of reversible operations is
likely to become more attractive.
If current trends continue this should occur sometime in the
2010 to 2020 timeframe.
If we are to reduce energy dissipation per logic operation
below ln 2 x *kT*
we will be *forced* to use reversible logic.

Nanotechnology
should let us build mole quantities of logic elements.
Unless energy dissipation per logic operation can be reduced
below *kT*, the raw cost of electricity
might well prove prohibitive and the
system might quickly overheat.

Even today the use of reversible logic operations can be a useful heuristic in the design of systems that use very little power. To achieve a completely reversible system (which erases no bits at all) is very difficult. As we allow more and more bits to be erased during normal system operation, it becomes easier and easier to design the system. Today's systems erase a bit for every logic operation they perform and are very dissipative. Systems that perform some operations in a reversible fashion can dissipate less energy and might prove competitive (particularly in niche applications) today.

Wikipedia has an article on reversible computing.

For an excellent review of the basic principles, see
*The Fundamental Limits
of Computation* by Charles H. Bennett and Rolf Landauer, Scientific
American, July 1985, pages 48-56 (38-53 in some versions). For the history, see
*Notes on the History of Reversible Computation* by
Charles Bennett, IBM J. Research and Development, Vol. 32, No. 1,
January 1988, pages 16-23.

A workshop on the Physics of Computation was held at MIT in 1981; the papers were printed in the April, June and December issues of the 1982 International Journal for Theoretical Physics, Volume 21.

The Physics and Computation workshop series was held for several years starting in 1992. See the final program for PhysComp '94. PhysComp '96 was held in Boston in November of 1996. These workshops covered reversible logic and several other areas related to physics and computation.

A popular article
is *Silicon in Reverse* by Peter Wayner, Byte Magazine, August 1994,
page 67.

In the last few years, several researchers independently realized that reversible logic could be implemented using conventional CMOS circuits. This has stimulated several research groups to pursue the subject.

Paul Vitanyi maintains a page with papers and links on reversible computing.

There is a related page about the Physics of Computation at MIT.

The April 1995 issue of the Proceedings of the IEEE (Vol. 83, No. 4, pages 493-700) is a special issue on Low-Power Electronics. It provides useful background information for those interested in reversible logic, even though it has little direct discussion of the subject.

Three articles that discuss some possible implementations of reversible logic
and provide references to further reading are
*Helical Logic*, by Ralph C. Merkle and K. Eric Drexler;
*Reversible electronic logic using switches (pdf)*, by Ralph C. Merkle,
Nanotechnology 4 (1993) pages 21-40; and
*Two types of mechanical reversible logic*, by Ralph C. Merkle, Nanotechnology
4 (1993) pages 114-131.

A 2006 article on reversible logic from the American Scientist is available on the web.

This brief introduction to reversible logic is provided courtesy of Ralph C. Merkle.

This page is part of the nanotechnology web site.