Non-Hermitian quantum annealing in the antiferromagnetic Ising chain

A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to {Mathematical expression} spins) that our approach leads to a significant reduction in the annealing time that is proportional to {Mathematical expression}, which is much less than the time (proportional to {Mathematical expression}) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms. © 2013 Springer Science+Business Media New York