Quantum Information Processing

, Volume 12, Issue 1, pp 611–623 | Cite as

How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies

  • Christopher Ferrie
  • Christopher E. GranadeEmail author
  • D. G. Cory


Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an important parameter in the Hamiltonian. Here, we explore how to design experiments so as to minimize error in the estimation of this parameter. While it has been shown that useful results may be obtained by minimizing the risk incurred by each experiment, such an approach is computationally intractable in general. Here, we motivate and derive heuristic strategies for experiment design that enjoy the same exponential scaling as fully optimized strategies. We then discuss generalizations to the case of finite relaxation times, T 2 < ∞.


Quantum process tomography Hamiltonian estimation Experiment design Parameter estimation Cramer–Rao bound Adaptive tomography 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Christopher Ferrie
    • 1
    • 2
  • Christopher E. Granade
    • 1
    • 3
    Email author
  • D. G. Cory
    • 1
    • 4
    • 5
  1. 1.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  3. 3.Department of PhysicsUniversity of WaterlooWaterlooCanada
  4. 4.Department of ChemistryUniversity of WaterlooWaterlooCanada
  5. 5.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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