© 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. Landauer¹⁹⁸⁶ 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 Toffoli¹⁹⁸⁷ 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. Feynman¹⁹⁹⁶ 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. Hall¹⁷⁴³ 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