Non-Hermitian quantum annealing in the antiferromagnetic Ising chain

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 $$N=1,024$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Non-Hermitian quantum annealing in the antiferromagnetic Ising chain

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0656-z
Publisher site
See Article on Publisher Site

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 $$N=1,024$$ 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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 19, 2013

References

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