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Projective measurements of a single two-level quantum mechanical system (aqubit) evolving under a time-independent Hamiltonian produce a probabilitydistribution that is periodic in the evolution time. The period of thisdistribution is an important parameter in the Hamiltonian. Here, we explore howto design experiments so as to minimize error in the estimation of thisparameter. While it has been shown that useful results may be obtained byminimizing the risk incurred by each experiment, such an approach iscomputationally intractable in general. Here, we motivate and derive heuristicstrategies for experiment design that enjoy the same exponential scaling asfully optimized strategies. We then discuss generalizations to the case offinite relaxation times, T_2 < \infty.

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