Energy consumption of probabilistic and quantum finite state verifiers

Irreversible steps in computation are associated with an erasure of information and thus, an increase in the entropy. In the case of a physical computer, this increase in entropy is associated with energy dissipation, although modern computers are nowhere near this lower bound and generate heat mostly due to other reasons. This work explores the reversibility properties of non-interactive verification systems with finite memory whose verifiers do quantum, deterministic or probabilistic computation. Definitions made in this work provide a framework in which questions about reversibility can be asked and answered. A method that eliminates some types of irreversibilities in probabilistic finite state verification systems is provided. Moreover, every type of irreversibility in such systems are conjectured to be eliminated as a conclusion.