Journal: Entropy

Article Title: Quantum Foundations of Classical Reversible Computing

doi: 10.3390/e23060701

Figure Lengend Snippet: Illustration of different types of computational operations O s t on a set C of 3 computational states. Examples shown here are partial functions— O ( c 3 ) is not defined. At upper-left is a conventional (deterministic but non-reversible) computational operation which merges two initially distinct computational states. At upper-right is a deterministic, reversible operation which is injective (one-to-one) over the subset A = { c 1 , c 2 } of initial states for which it is defined. At lower-right is a stochastic but reversible operation which does not merge any states, but splits the state c 2 (with some nonzero probability to transition to either c 1 or c 3 ). Finally, at lower-left is a stochastic, irreversible operation which includes both splits and merges.

Article Snippet: The significance of the two RC theorems together is that, in order to avoid the otherwise-necessary entropy increase resulting from Landauer’s Principle when performing isolated computational operations on subsystems in the context of larger deterministic computations, one must confine oneself to the above two cases (unconditionally reversible operations, and/or conditionally reversible operations that have a satisfied condition for reversibility).

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