Study of Optimization Problems by Quantum Annealing
@article{Kadowaki2002StudyOO,
title={Study of Optimization Problems by Quantum Annealing},
author={Tadashi Kadowaki},
journal={arXiv: Quantum Physics},
year={2002}
}We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. The idea is tested by the two models, the transverse Ising model and the traveling salesman problem (TSP). Adding the transverse field to the Ising model is a simple way to introduce quantum fluctuations. The strength of the transverse field is controlled as a function of time similarly to the temperature in the conventional method. TSP can be…
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References
SHOWING 1-10 OF 71 REFERENCES
Quantum annealing in the transverse Ising model
- Physics
- 1998
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…
The Monte Carlo Simulation
- Physics
- 1989
The Monte Carlo method, as applied to charge transport in semiconductors, consists of a simulation of the motion of one or more electrons inside the crystal, subject to the action of external forces…
Quantum Ising Phases and Transitions in Transverse Ising Models
- Physics
- 1996
Introduction.- Transverse Ising Chain (Pure System).- Transverse Ising System in Higher Dimensions (Pure Systems).- ANNNI Model in Transverse Field.- Dilute and Random Transverse Ising Systems.-…
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Computer Science
- 1978
It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.
The Design and Analysis of Computer Algorithms
- Computer Science
- 1974
This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Introduction to the theory of neural computation
- Computer ScienceThe advanced book program
- 1991
This book is a detailed, logically-developed treatment that covers the theory and uses of collective computational networks, including associative memory, feed forward networks, and unsupervised learning.
Likes and Dislikes
- Political Science
- 1996
Many people wonder what they can do about improving their accent. The key to speaking well is listening. Try listening for sound rather than for content and think about intonation – that is, the…
Higher Transcendental Functions
- PsychologyNature
- 1955
Higher Transcendental FunctionsBased, in part, on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project. Vol. 1. Pp. xxvi + 302. 52s. Vol. 2. Pp. xvii + 396.…
Biological Cybernetics
- Political ScienceNature
- 1972
Information and Control in the Living Organism. By Bernhard Hassenstein. Pp. viii + 159. (Chapman and Hall: London, December 1971.) £1.30.