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...

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Bibliographic Details
Published inQuantum information processing Vol. 13; no. 2; pp. 371 - 389
Main Authors Nesterov, Alexander I., Berman, Gennady P., Zepeda, Juan C. Beas, Bishop, Alan R.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2014
Springer
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-013-0656-z