Abstract
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H=\ensuremath{\theta}{H}_{0}$, we estimate $\ensuremath{\theta}$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\ensuremath{\theta}$ whose variance has been decreased in proportion to the time of evolution under $H$. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference frame alignment are also studied within the adaptive approach.
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