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Foundations of Generalized Reversible Computing

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 10301)

Abstract

Information loss from a computation implies energy dissipation due to Landauer’s Principle. Thus, increasing the amount of useful computational work that can be accomplished within a given energy budget will eventually require increasing the degree to which our computing technologies avoid information loss, i.e., are logically reversible. But the traditional definition of logical reversibility is actually more restrictive than is necessary to avoid information loss and energy dissipation due to Landauer’s Principle. As a result, the operations that have traditionally been viewed as the atomic elements of reversible logic, such as Toffoli gates, are not really the simplest primitives that one can use for the design of reversible hardware. Arguably, a complete theoretical framework for reversible computing should provide a more general, parsimonious foundation for practical engineering. To this end, we use a rigorous quantitative formulation of Landauer’s Principle to develop the theory of Generalized Reversible Computing (GRC), which precisely characterizes the minimum requirements for a computation to avoid information loss and the consequent energy dissipation, showing that a much broader range of computations are, in fact, reversible than is acknowledged by traditional reversible computing theory. This paper summarizes the foundations of GRC theory and briefly presents a few of its applications.

Keywords

  • Landauer’s Principle
  • Foundations of reversible computing
  • Logical reversibility
  • Reversible logic models
  • Reversible hardware design
  • Conditional reversibility
  • Generalized reversible computing

M.P. Frank—This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, and by the Advanced Simulation and Computing program under the U.S. Department of Energy’s National Nuclear Security Administration (NNSA). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for NNSA under contract DE-AC04-94AL85000. Approved for unclassified unlimited release SAND2017-3513 C.

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Notes

  1. 1.

    Per [1], minimum gate energies are expected to bottom out at around the 40–80 \(k_\mathrm{B}T\) (1–2 eV) level (where \(k_\mathrm{B}\) is Boltzmann’s constant, and T is operating temperature); while typical total \(CV^2\) node energies (where C is node capacitance, and V is logic swing voltage) may level off at a corresponding higher range of 1–2 keV.

  2. 2.

    Although quantum physics does not yet incorporate a description of gravity, it’s expected that even a full theory of quantum gravity would still exhibit unitarity.

  3. 3.

    Note that this is a different sense of the word “nondeterministic” than is commonly used in computational complexity theory, when referring to, for example, nondeterministic Turing machines, which conceptually evaluate all of their possible future computational trajectories in parallel. Here, when we use the word “nondeterministic,” we mean it simply in the physicist’s sense, to refer to randomizing or stochastic operations; i.e., those whose result is uncertain.

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Frank, M.P. (2017). Foundations of Generalized Reversible Computing. In: Phillips, I., Rahaman, H. (eds) Reversible Computation. RC 2017. Lecture Notes in Computer Science(), vol 10301. Springer, Cham. https://doi.org/10.1007/978-3-319-59936-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-59936-6_2

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