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 \(N=1,024\) spins) that our approach leads to a significant reduction in the annealing time that is proportional to \(\ln N\), which is much less than the time (proportional to \(N^2\)) 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.
quantum annealing ground states critical points quantum theory adiabatic quantum computation