Development of time dependent DMRG method for higher dimensional systems and its application to quantum annealing

In order to investigate quantum dynamics on higher dimensional strongly correlated systems, we have developed new kind of the time dependent DMRG (tDMRG) method using the kernel polynomial method (KPM). In our tDMRG method, a time depending state is directly calculated by the KPM. By a three-term recursive formula of special functions, we can perform effective tDMRG calculations. Also, our tDMRG calculations give accurate results as long as we employ large enough DMRG truncation number. In the present study, we have applied our tDMRG method to quantum annealing which is a kind of quantum computing for optimization problems. In the quantum annealing, the Hamiltonian is constructed by a two-dimensional Ising model with transverse magnetic field. Our tDMRG calculations of the quantum annealing give correct answer of optimization problems by using relatively small DMRG truncation number. Thus, our tDMRG method is suitable for numerical studies of the quantum annealing.