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 $$N=1,024$$ N = 1 , 024 spins) that our approach leads to a significant reduction in the annealing time that is proportional to $$\ln N$$ ln N , which is much less than the time (proportional to $$N^2$$ 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 Information Processing – Springer Journals
Published: Oct 19, 2013
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