NV-Center Based Digital Quantum Simulation of a Quantum Phase Transition in Topological Insulators

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 phase 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.