Adaptive phase estimation through a genetic algorithm

Abstract

Quantum metrology is one of the most relevant applications of quantum information theory to quantum technologies. Here, quantum probes are exploited to overcome classical bounds in the estimation of unknown parameters. In this context, phase estimation, where the unknown parameter is a phase shift between two modes of a quantum system, is a fundamental problem. In practical and realistic applications, it is necessary to devise methods to optimally estimate an unknown phase shift by using a limited number of probes. Here we introduce and experimentally demonstrate a machine learning-based approach for the adaptive estimation of a phase shift in a Mach-Zehnder interferometer, tailored for optimal performances with limited resources. The employed technique is a genetic algorithm used to devise the optimal feedback phases employed during the estimation in an offline fashion. The results show the capability to retrieve the true value of the phase by using few photons, and to reach the sensitivity bounds in such small probe regime. We finally investigate the robustness of the protocol with respect to common experimental errors, showing that the protocol can be adapted to a noisy scenario. Such approach promises to be a useful tool for more complex and general tasks where optimization of feedback parameters is required.

Optimal Scheme for Quantum Metrology

“…Peng and Fan [175] further proposed an ansatz that reduces the complexity to N 4 . Experimentally, an offline scheme based on the PSO algorithm has been realized by Lumino et al [176] Other optimization methods, such as the genetic algorithm [177] and the differential evolution (DE) algorithm, [178] have also been used in the offline adaptive measurement. Compared to the PSO algorithm, the performance of the DE algorithm is more robust, and the DE algorithm also works better with a large photon number.…”

Experimental adaptive Bayesian estimation of multiple phases with limited data

“…Adaptive protocols represent a relevant tool in phase estimation process. Indeed, the adoption of adaptive strategies becomes a crucial requirement even in the single-parameter case to optimize the algorithm performances [11][12][13]16,18,19,21,22,63,70,71 , with the aim of achieving the ultimate bounds provided by the Cramér-Rao inequality for small values of N 18 . Furthermore, in more complex systems characterized by a phase-dependent Fisher information matrix, adaptive strategies become crucial to reach equal performances for all values of the unknown parameter(s) 34 .…”

“…A possible approach towards the protocol optimization is that of exploiting adaptive strategies. These have been successfully employed in single-parameter estimation 8,[11][12][13][14][15][16][17][18][19][20] . In this regard, machine learning (ML) approaches have provided a significant speed up in the saturation of the ultimate bounds 8,18,19,[21][22][23] .…”

Calibration of Multiparameter Sensors via Machine Learning at the Single-Photon Level

“…These are capable of handling large data sets and of solving tasks for which they have not been explicitly programmed; applications range from stock-price predictions [11,12] to the analysis of medical diseases [13]. In the past few years, several applications of machine-learning methods in the quantum domain have been reported [14][15][16], including state and unitary tomography [17][18][19][20][21][22][23][24][25], the design of quantum experiments [26][27][28][29][30][31][32], the validation of quantum technology [33][34][35], the identification of quantum features [36,37], and the adaptive control of quantum devices [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Also, photonic platforms can be exploited for the realization of machine-learning protocols [55,56]...…”