Abstract
Motived by the new complexity conjecture [1] suggesting that the fastest computer in nature are the black holes. We study the action growth rate for a variety of four-dimensional regular black holes such as Hayward, Bardeen and the new class proposed in [2]. Generally, we show that action growth rates of the Wheeler-De Witt patch are finite for such black hole configurations at the late time approach and satisfy the Lloyd bound on the rate of quantum computation. Also, the case of three dimensions space is investigated. In each regular black hole configuration, we found that the form of the Lloyd bound formula remains unaltered but the energy is modified due to the effect of the nonlinear electrodynamics where some extra-therm have appeared in the total growth action.
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