  In a seminal paper by Brown et al. [Phys. Rev. Lett. 116, no. 19, 191301
(2016)] a new conjecture was proposed, namely it was argued that the quantum
complexity of a holographic state is equal to action of a Wheeler-DeWitt patch
in the late time limit suggesting that the fastest computer in nature are the
black holes. Motivated by this conjecture, in the present paper, we study the
action growth rate for different types of black holes such as dyonic, nonlinear
charge, stringy hair, black hole with a global monopole and a cosmic string. In
general we find that action growth rates of the Wheeler-DeWitt patch is finite
for these black holes at the late time approach and satisfy the Lloyd bound on
the rate of quantum computation. Furthermore, in the case of a charged as well
as the neutral black hole with a global monopole and a conical defect we show
that the form of the Lloyd bound relation remains unaltered but the energy is
modified due to the nontrivial global topology of the spacetime.

General Relativity and Quantum Cosmology;High Energy Physics - Theory