Parameter Estimation with Mixed-State Quantum Computation

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 $H=\theta H_0$, we estimate $\theta$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\theta$ 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 discussed within the adaptive approach.

12 pages. Improved introduction and technical details moved to Appendix

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