We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N , where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NPcomplete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.
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.
We consider the non-Hermitian quantum annealing for the one-dimensional Ising spin chain, and for a large number of qubits. We show that the annealing time is significanlty reduced for the non-Hermitian algorithm in comparison with the Hermitian one. We also demonstrate the relation of the non-Hermitian quantum annealing with the superradiance transition in this system.
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