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Quantum-state diffusion: Application to Bayesian hierarchical modeling

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  • Zarezadeh, Z.
  • Costantini, G.

Abstract

The geometrical interpretation of density operators for open quantum system is investigated. After the discussion of stochastic mapping and the purifying lifts of curves of density matrices, the quantum analog of the classical recipe for the construction of an infinitesimal generator has been established. Despite the main contribution of the present paper in providing the formal expression of such generator, a simple experimental realization of a geometrically intuitive approach to variational inference also established. Nonetheless, the numerical results given here are competitive with those from the other methods used for quantum and classical systems and provide insight into the origin of properties of open quantum systems.

Suggested Citation

  • Zarezadeh, Z. & Costantini, G., 2021. "Quantum-state diffusion: Application to Bayesian hierarchical modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    • Handle: RePEc:eee:phsmap:v:584:y:2021:i:c:s0378437121006555
    DOI: 10.1016/j.physa.2021.126382
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    References listed on IDEAS

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    1. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
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