Learning feedback control strategies for quantum metrology

Abstract

We consider the problem of frequency estimation for a single bosonic field evolving under a squeezing Hamiltonian and continuously monitored via homodyne detection. In particular, we exploit reinforcement learning techniques to devise feedback control strategies achieving increased estimation precision. We show that the feedback control determined by the neural network greatly surpasses in the long time limit the performances of both the "no-control" and the "standard openloop control" strategies, that we considered as benchmarks. We indeed observe how the devised strategy is able to optimize the nontrivial estimation problem by preparing a large fraction of trajectories corresponding to more sensitive quantum conditional states.

Noise-assisted and monitoring-enhanced quantum bath tagging

“…The role of such an extra environment is twofold: on one hand, the presence of A is used as a way to positively interfere with the S-E coupling in an effort to increase the distinguishability among the quantum trajectories associated with the two hypothesis of the problem; on the second hand, A is employed to set up an indirect, continuous monitoring of the evolution of S, hence allowing us to acquire information about E in real time and not just at the end of the interaction interval. Continuous monitoring of quantum systems [24,25] has indeed been proven useful in the context of quantum metrology: in particular several works have either discussed the fundamental statistical tools to assess the precision achievable in this framework [26][27][28][29][30][31][32][33], and presenting practical estimation strategies [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The theoretical framework needed to assess hypothesis testing protocols has been put forward first by Tsang [50] and then by Kiilerich and Molmer [51].…”

Exponential precision by reaching a quantum critical point

“…It has also been shown [15,16] that, in spite of the critical slowing down, the framework of critical quantum metrology makes it possible to achieve the Heisenberg scaling, where the QFI grows quadratically in time and number of probes. Recent works [16][17][18][19][20][21][22][23][24] have shown that the framework of critical quantum metrology can be applied to a broad class of quantum optical models. Current solid-state and atomic technology allow for the implementation of these models in a controllable way, where their parameters can be tuned in real time.…”