Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model

We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NP-complete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.
Comment: 14 pages, 12 figures