Nitrogen-vacancy centers in diamond are ideal platforms for quantum simulation, which allows one to handle problems that are intractable theoretically or experimentally. Here we propose a digital quantum simulation scheme to simulate the quantum phas
e transition occurring in an ultrathin topological insulator film placed in a parallel magnetic field [Zyuzin textit{et al.}, Phys. Rev. B textbf{83}, 245428 (2011)]. The quantum simulator employs high quality spin qubits achievable in nitrogen-vacancy centers and can be realized with existing technology. The problem can be mapped onto the Hamiltonian of two entangled qubits represented by the electron and nuclear spins. The simulation uses the Trotter algorithm, with an operation time of the order of 100 $mu$s for each individual run.
To implement reliable quantum information processing, quantum gates have to be protected together with the qubits from decoherence. Here we demonstrate experimentally on nitrogen-vacancy system that by using continuous wave dynamical decoupling metho
d, not only the coherence time is prolonged by about 20 times, but also the quantum gates is protected for the duration of controlling time. This protocol shares the merits of retaining the superiority of prolonging the coherence time and at the same time easily combining with quantum logic tasks. It is expected to be useful in task where duration of quantum controlling exceeds far beyond the dephasing time.
