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

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Abstract

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 < ∞.

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Authors and Affiliations

  1. Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada

    Christopher Ferrie, Christopher E. Granade & D. G. Cory

  2. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada

    Christopher Ferrie

  3. Department of Physics, University of Waterloo, Waterloo, ON, Canada

    Christopher E. Granade

  4. Department of Chemistry, University of Waterloo, Waterloo, ON, Canada

    D. G. Cory

  5. Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada

    D. G. Cory

Authors
  1. Christopher Ferrie
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  2. Christopher E. Granade
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  3. D. G. Cory
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Correspondence to Christopher E. Granade.

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Ferrie, C., Granade, C.E. & Cory, D.G. How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies. Quantum Inf Process 12, 611–623 (2013). https://doi.org/10.1007/s11128-012-0407-6

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  • DOI: https://doi.org/10.1007/s11128-012-0407-6

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