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Quantum Annealing of a ±J Spin Glass and a Kinetically Constrained System

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Quantum Annealing and Other Optimization Methods

Part of the book series: Lecture Notes in Physics ((LNP,volume 679))

Abstract

Thermal annealing [1] is known to be a very general and useful method for obtaining approximate solutions of multi-variable optimization problems. Such a problem consists of the minimization of a multi-variable function (costfunction) with respect to its variables (sometimes obeying a given set of constraints). The cost-function landscape are often very rugged, consisting of local minima surrounded by high cost-barriers. In such cases optimization using iterative minimization heuristics can fail miserably by getting trapped into an arbitrarily shallow minimum. In thermal annealing a fictitious thermal fluctuation is introduced into the minimization dynamics to generate possibility of going uphill. This enables the system to get out of the shallow traps and explore the landscape more widely to find out a reasonably deep minimum for settling down. The thermal fluctuation is eventually, but slowly, reduced to zero and one ends up, to a good approximation, with a globally optimized solution.

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Authors and Affiliations

  1. Theoretical Condensed Matter Physics Division and Center for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata, 700064, India

    Arnab Das & Bikas K. Chakrabarti

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  1. Arnab Das
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  2. Bikas K. Chakrabarti
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Arnab Das Bikas K. Chakrabarti

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Das, A., K. Chakrabarti, B. Quantum Annealing of a ±J Spin Glass and a Kinetically Constrained System. In: Das, A., K. Chakrabarti, B. (eds) Quantum Annealing and Other Optimization Methods. Lecture Notes in Physics, vol 679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526216_9

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  • DOI: https://doi.org/10.1007/11526216_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27987-7

  • Online ISBN: 978-3-540-31515-5

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