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It has been recently reported that classical systems have speed limit forstate evolution, although such a concept of speed limit had been considered tobe unique to quantum systems. Owing to the speed limit for classical system,the lower bound for calculation time of simulated annealing with desiredcalculation accuracy can be derived. However, such a lower bound does not workas a criterion for completion of calculation in a practical time. In thispaper, we derive an inequality for classical system analogous to the quantumadiabatic theorem that gives calculation time for an accuracy-guaranteedfluctuation-exploiting computation. The trade-off relation between calculationtime and accuracy is given in the form tolerable in practical use.

Upper bound inequality for calculation time in simulated annealing analogous to adiabatic theorem in quantum systems