Quantum Annealing in the Transverse Ising Model
1998/04/25 by Tadashi Kadowaki, Hidetoshi Nishimori · 254 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.58.5355
published as Phys. Rev. E 58, 5355 (1998) · 15 pages, RevTeX, 8 figures
arxiv created 1998/04/25 · openalex publication_date 1998/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract
We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schrödinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule.
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