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## Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain

Alexander I. Nesterov, Gennady P. Berman, Juan C. Beas Zepeda, Alan R. Bishop

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=1024 spins) that our approach leads to a significant reduction of 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.

http://arxiv.org/abs/1302.6555
Quantum Physics (quant-ph); Mathematical Physics (math-ph)