Study of quantum annealing by simulating the time evolution of flux qubits

In this thesis, we study the operation of existing quantum annealers by simulating the real-time dynamics of two coupled flux qubits based on SQUIDs (superconducting quantum interference devices) during quantum annealing processes. We investigate two aspects. First, we study the influence of the higher energy levels which are neglected when deriving the qubit Hamiltonian from the superconducting circuit model including the tunable coupler. Second, we investigate the influence of an environment on the qubit system during quantum annealing. For the latter, we examine two different models for the environment, a generic spin bath and non-interacting two-level systems. For simulating the dynamics, we use the Suzuki-Trotter product-formula algorithm to solve the time-dependent Schrödinger equation numerically. We find that the higher energy levels as well as the presence of the tunable coupler have little influence on the performance of the quantum annealing process for most of the investigated problem instances, suggesting that the two-level approximation works very well. However, we find that for a particular class of instances, the results of the SQUID model and the qubit model show certain deviations. Additionally, we perform experiments on the D-Wave 2000Q quantum annealer. Our study of the two models for the environment suggests that the model of non-interacting two-level systems is better suited to describe the data obtained from the real device than the generic spin bath model