Efficient estimation of resonant coupling between quantum systems

Adaptive Bayesian algorithm for achieving a desired magneto-sensitive transition

Bayesian methods that utilize Bayes' theorem to update the knowledge of desired parameters after each measurement are used in a wide range of quantum science. For various applications in quantum science, efficiently and accurately achieving a quantum transition frequency is essential. However, the exact relation between a desired transition frequency and the controllable experimental parameters is usually absent. Here, we propose an efficient scheme to search the suitable conditions for a desired magneto-sensitive transition via an adaptive Bayesian algorithm and experimentally demonstrate it by using coherent population trapping in an ensemble of laser-cooled ⁸⁷Rb atoms. The transition frequency is controlled by an external magnetic field, which can be tuned in realtime by applying a d.c. voltage. Through an adaptive Bayesian algorithm, the voltage can automatically converge to the desired one from a random initial value only after few iterations (N ≥ 10). The response time is limited by the time of obtaining the spectrum signal, which is about 50 s for 10 iterations in our experiment. In particular, when the relation between the target frequency and the applied voltage is nonlinear (e.g., quadratic), our algorithm shows significant advantages over traditional methods. This work provides a simple and efficient way to determine a transition frequency, which can be widely applied in the fields of precision spectroscopy, such as atomic clocks, magnetometers, and nuclear magnetic resonance.

Quantum Probes for Ohmic Environments at Thermal Equilibrium

It is often the case that the environment of a quantum system may be described as a bath of oscillators with an ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or to tailor quantum information protocols. Recently, the use of quantum probes in characterizing ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to a complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision attainable by quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e., values of the order ωc≲T (in natural units). For larger values of ωc, decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.

Efficient Bayesian Phase Estimation

We introduce a new method called rejection filtering that we use to perform adaptive Bayesian phase estimation. Our approach has several advantages: it is classically efficient, easy to implement, achieves Heisenberg limited scaling, resists depolarizing noise, tracks time-dependent eigenstates, recovers from failures, and can be run on a field programmable gate array. It also outperforms existing iterative phase estimation algorithms such as Kitaev's method.