Title: Quantum annealing and its variants: Application to quadratic unconstrained optimization
Abstract: We study and compare the performance of the numerical implementation of quantum annealing and physical quantum annealing systems from D-Wave Quantum Systems Inc. for solving a specially constructed set of hard 2-SAT problems using three metrics: the probability of the algorithm to solve the problem, its ability to find all the solutions to the problem if the problem has more than one solution, and the scaling of the time to solution as a function of the problem size. Furthermore, by means of simulations, we introduce two modifications in the standard quantum annealing algorithm, and gauge the performance of the modified algorithms. These modifications are the addition of a trigger Hamiltonian to the standard quantum annealing Hamiltonian, or a change in the initial Hamiltonian of the annealing Hamiltonian. We choose the trigger Hamiltonian to have either ferromagnetic or antiferromagnetic transverse couplings, while the additional higher-order couplings added to the typically chosen initial Hamiltonian are ferromagnetic.
1 окт 2024
