Reversible Computing

Reversible computing is a model of computing where the computational process to some extent is reversible, i.e., time-invertible. A necessary condition for reversibility of a computational model is that the relation of the mapping states of transition functions to their successors should at all times be one-to-one. Reversible computing is generally considered an unconventional form of computing.

There are two major, closely related, types of reversibility that are of particular interest for this purpose: physical reversibility and logical reversibility.

A process is said to be physically reversible if it results in no increase in physical entropy; it is isentropic. These circuits are also referred to as charge recovery logic or adiabatic computing. Although in practice no nonstationary physical process can be exactly physically reversible or isentropic, there is no known limit to the closeness with which we can approach perfect reversibility, in systems that are sufficiently well-isolated from interactions with unknown external environments, when the laws of physics describing the system's evolution are precisely known.

Probably the largest motivation for the study of technologies aimed at actually implementing reversible computing is that they offer what is predicted to be the only potential way to improve the energy efficiency of computers beyond the fundamental von Neumann-Landauer limit of kT ln(2) energy dissipated per irreversible bit operation.

As was first argued by Rolf Landauer of IBM, in order for a computational process to be physically reversible, it must also be logically reversible. Landauer's principle is the loosely formulated notion that the erasure of n bits of information must always incur a cost of nk ln(2) in thermodynamic entropy. A discrete, deterministic computational process is said to be logically reversible if the transition function that maps old computational states to new ones is a one-to-one function; i.e. the output logical states uniquely defines the input logical states of the computational operation.

For computational processes that are nondeterministic (in the sense of being probabilistic or random), the relation between old and new states is not a single-valued function, and the requirement needed to obtain physical reversibility becomes a slightly weaker condition, namely that the size of a given ensemble of possible initial computational states does not decrease, on average, as the computation proceeds forwards.

Read more about Reversible ComputingThe Reversibility of Physics and Reversible Computing, Reversible Circuits

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Reversible Computing - Reversible Circuits
... To implement reversible computation, estimate its cost, and to judge its limits, it is formalized it in terms of gate-level circuits ... For example, the inverter (logic gate) (NOT) gate is reversible because it can be undone ... However, a reversible version of the XOR gate --- the Controlled NOT gate(CNOT) --- can be defined by preserving one of the inputs ...