Non-Hermitian quantum annealing in the antiferromagnetic Ising chain

• Published in: Quantum 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
• Language: English
• Published: New York Springer US 01.02.2014; Springer
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Classical and quantum physics: mechanics and fields; Computer science; control theory; systems; Data Structures and Information Theory; Exact sciences and technology; Mathematical Physics; Physics; Physics and Astronomy; Quantum computation; Quantum Computing; Quantum information; Quantum Information Technology; Quantum Physics; Spintronics; Theoretical computing; Quantum annealing; Adiabatic quantum computation; Ground states; Critical points; Quantum theory; Adiabatic passage; Annealing; Quantum algorithm; Hermite interpolation; Critical point; Quantum computation; Ising model; NP complete problem
• ISSN: 1570-0755; 1573-1332
• DOI: 10.1007/s11128-013-0656-z

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.