**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**10.2.4.1 Reversible
Computers**

Computers may be thought of as engines for transforming free
energy into waste heat and mathematical work.^{296}
Early pioneers of computing theory^{1984,1985
}believed that each step in a a computer's binary computation required
a minimum energy expenditure of ~kT ln(2) ~3 zJ/bit at T = 310 K. In 1961, R.
Landauer^{1986} argued that it
was the erasure of information, not computation per se, that generates waste
heat. It is now known that computers can in principle do an arbitrarily large
amount of reliable computation per kT of energy dissipated.^{296}
Following Landauer's insight, Fredkin and Toffoli^{1987}
suggested an idealized "ballistic computer" that could, in theory, compute at
finite speed with zero energy dissipation and zero error. A more pragmatic family
of models are the "Brownian computers"^{296}
in which thermal noise pushes system elements in a random walk throughout the
entire accessible portion of the computer's configuration space; in these models,
energy dissipation trends to zero only in the limit of zero speed. Both ballistic
and Brownian computers require that all computations are logically reversible,
with no irreversible bit erasures and no machine state having more than one
logical predecessor -- that is, the output uniquely specifies the input.^{10}

One simple implementation of reversible computing is the retractile
cascade.^{10,296,1743}
In a retractile cascade, all inputs and all intermediate states leading to a
result are retained during the course of a computation. After the computation
is complete, the final result is copied to an output register, requiring the
irreversible erasure of only enough bits in the output register to hold a copy
of the final result, which need cost no more than kT ln(2) per erased bit. The
computation is then reversed, step by step, culminating with the original inputs;
the slower the reversible steps are performed, the less energy they may dissipate
(but the longer the computation takes). Schematics for a retractile AND gate,
adder, shifter, and programmable logic array have been published,^{1743}
and in 1998 a reversible processor based on a modern RISC architecture was being
designed.^{1994} A conventional
computer architecture, implemented without regard to reversibility, may perform
0.1-1 bit erasures/gate-cycle; by comparison, a retractile computer might average
<10^{-4} bit erasures/gate-cycle.^{1743}
During the reversible portion of the computation, Drexler's exemplar rod logic
design (Section 10.2.1) employs a retractile cascade
that reduces room-temperature energy dissipation from the "classical" minimum
of ~0.7 kT down to ~0.003 kT per gate-cycle. In the limit of slow motion, all
identified energy dissipation mechanisms in combinatorial rod logic systems
approach zero.^{10} The Tour-Seminario
electrostatic field switch might attain ~10^{-5} kT per gate-cycle
at room temperature; low-temperature helical logic (Section
10.2.2.3) could achieve ~10^{-7} kT per gate-cycle. Feynman^{1996}
notes that the minimum free energy required for a reversible computation may
be made independent of the complexity or number of steps in the calculation,
and may be as small as ~kT per bit of the output answer.

J.S. Hall^{1743}
suggests two principal design rules for efficient nanocomputers:

1. erase as few bits as possible, and

2. eliminate entropy loss in operations that do not erase bits.

Many reviews of reversible computing have been published.^{296,713,1097,1743,1988,1989}

Last updated on 24 February 2003