Parameter estimation with mixed-state quantum computation

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=θH₀, we estimate θ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of θ 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.