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Quantum stochastic optimization

Author

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  • Apolloni, B.
  • Carvalho, C.
  • de Falco, D.

Abstract

We propose a combinatorial optimization procedure based on the physical idea of using the quantum tunnel effect to allow the search of global minima of a function of many Boolean variables to escape from poor local minima. More specifically, the function V to be minimized is viewed as the potential energy term in a Schrodinger Hamiltonian H for a quantum spin 1/2 system, the kinetic energy term being the generator of a random walk tailored to the neighborhood structure associated with V The distorted random walk associated with (a suitable approximation of) the ground state eigenfunction of H defines then our approximate optimization strategy. A numerical application to the graph partitioning problem is presented.

Suggested Citation

  • Apolloni, B. & Carvalho, C. & de Falco, D., 1989. "Quantum stochastic optimization," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 233-244, December.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:2:p:233-244
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    Cited by:

    1. Adam Bouland & Wim van Dam & Hamed Joorati & Iordanis Kerenidis & Anupam Prakash, 2020. "Prospects and challenges of quantum finance," Papers 2011.06492, arXiv.org.
    2. Presilla, Carlo & Ostilli, Massimo, 2019. "Phase transitions and gaps in quantum random energy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 57-64.

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