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On Grover’s search algorithm from a quantum information geometry viewpoint

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  • Cafaro, Carlo
  • Mancini, Stefano

Abstract

We present an information geometric characterization of Grover’s quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner–Yanase quantum information metric. We then show that the quantum searching problem can be recast in an information geometric framework where Grover’s dynamics is characterized by a geodesic on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover’s algorithm. We also discuss possible deviations from Grover’s algorithm within this quantum information geometric setting.

Suggested Citation

  • Cafaro, Carlo & Mancini, Stefano, 2012. "On Grover’s search algorithm from a quantum information geometry viewpoint," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1610-1625.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1610-1625
    DOI: 10.1016/j.physa.2011.09.018
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    References listed on IDEAS

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    1. Cafaro, C. & Ali, S.A., 2008. "Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6876-6894.
    2. Janke, W. & Johnston, D.A. & Kenna, R., 2004. "Information geometry and phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 181-186.
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    Cited by:

    1. Razavian, Sholeh & Paris, Matteo G.A., 2019. "Quantum metrology out of equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 825-833.
    2. Cafaro, Carlo, 2017. "Geometric algebra and information geometry for quantum computational software," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 154-196.

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