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arXiv · 1302.6555

Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain

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

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.

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Alexander I. Nesterov, Gennady P. Berman, Juan C. Beas Zepeda, Alan R. Bishop. 2013-02-26. Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain. https://doi.org/10.1007/s11128-013-0656-z

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