  The system undergoes adiabatic evolution when its population in the
instantaneous eigenbasis of its time-dependent Hamiltonian changes only
negligibly. Realization of such dynamics requires slow-enough changes of the
parameters of the Hamiltonian, a task that can be hard to achieve near quantum
critical points. A powerful alternative is provided by the counterdiabatic
modification of the Hamiltonian allowing for an arbitrarily quick
implementation of the adiabatic dynamics. Such a counterdiabatic driving
protocol has been recently proposed for the quantum Ising model [A. del Campo
et al., Phys. Rev. Lett. 109, 115703 (2012)]. We derive an exact closed-form
expression for all the coefficients of the counterdiabatic Ising Hamiltonian.
We also discuss two approximations to the exact counterdiabatic Ising
Hamiltonian quantifying their efficiency of the dynamical preparation of the
desired ground state. In particular, these studies show how quantum criticality
enhances finite-size effects in the counterdiabatic dynamics.
