Counterdiabatic route for preparation of state with long-range topological order

We propose here a counterdiabatic (CD) strategy for the fast preparation of a state with long-range topological order by magnetic field tuning of an initial separable state. For concreteness, we consider the ground state of the honeycomb Kitaev model whose long-range topological order together with the anyonic excitations make it an interesting candidate for fault-tolerant universal quantum computation and storage. We implement an approximate local CD perturbation having the form of the off-diagonal exchange interactions in Kitaev Hamiltonians. The counterdiabatically produced state is found to have a high fidelity $(\ensuremath{\gtrsim}0.5)$ and retains numerous desired entanglement properties while giving a speed-up of the order of ${10}⁶$. In our study of up to 24-spin clusters we found the fidelity is constrained by the spectral gap rather than the system size.