Superconducting flux qubits compared to ideal two-level systems as building blocks for quantum annealers

Quantum annealers provide a promising approach for solving optimization problems.The theory of quantum annealing is fundamentally different from gate-based quantum computing: In quantum annealing, the system is prepared in a known ground state of an initial Hamiltonian, then this Hamiltonian is adiabatically transformed into the final Hamiltonian whose ground state corresponds to the solution of the given problem.Quantum annealing works well in theory if the qubits can be modeled as two-level systems. However, in real devices, the qubits are not based on perfect two-level systems, but on a two-dimensional subspace of a larger system. This makes approximations in analytic calculations unavoidable.With a simulation utilizing the Suzuki-Trotter product-formula approach to solve the time-dependent Schrödinger equation, the time-evolution of the full state of such a device based on superconducting flux qubits is investigated and compared to the ideal two-level system