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Quantum Annealing in the Transverse Ising Model

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arxiv cond-mat/9804280 v1 pith:MSYVD5PL submitted 1998-04-25 cond-mat.stat-mech cond-mat.dis-nn

Tadashi Kadowaki , Hidetoshi Nishimori This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.dis-nn
keywords annealingquantumfluctuationsstatetransverseconventionalgroundising
verification ladder T0 review T1 audit T2 compute T3 formal
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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 Schr\"odinger 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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Cited by 3 Pith papers

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  1. Non-Hermitian Quantum Adiabatic Algorithm

    quant-ph 2026-07 conditional novelty 7.0 of 10

    A history-decoupled Hamiltonian mapping makes non-Hermitian adiabatic quantum optimization pseudospectrally stable, achieving polynomial-time (per configuration) evolution on the CK maximum-independent-set benchmarks.

  2. Leveraging Landau-Zener-St\"uckelberg interference for accelerating diabatic quantum annealing

    quant-ph 2026-06 unverdicted novelty 6.0 of 10

    Landau-Zener-Stückelberg interference enables a reduced-parameter variational ansatz for diabatic quantum annealing that permits polynomial-time classical schedule optimization and yields numerical speedups over adiab...

  3. Erasing Classical Memory with Quantum Fluctuations: Shannon Information Entropy of Reverse Quantum Annealing

    quant-ph 2025-09 conditional novelty 5.0 of 10

    Shannon entropy of magnetic domain-wall positions, measured on three D-Wave quantum annealers, reveals a crossover from full memory retention to full memory loss as the transverse field increases, shifting with anneal...

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