Experimental adaptive Bayesian estimation of multiple phases with limited data

Abstract

Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.

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

“…The integrated device under study is a three-arm interferometer realized by the femtosecond-laser-writing technique [60,61] and able to perform multiphase estimation protocols [51,62]. The circuit is composed by a sequence of two three-arm beam splitters (tritters) realized through a two-dimensional geometry decomposition and interposed with three internal arms encoding two independent optical phase shifts φ = ( φ 1 , φ 2 ) of two of the arms with respect to the third one (reference).…”

“…Therefore, in the standard characterization, a theoretical model of the circuit is necessary to recover the output probabilities through a fit of the measured probabilities. This, in turn, allows us to extrapolate the dynamic and static parameters of the chip [51,62]. Conversely, the aim of this work is to avoid relying on knowledge about both the theoretical model of the circuit and the response function in Eq.…”

“…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]...…”

Femtosecond laser micromachining for integrated quantum photonics

“…Three-arm interferometers, equipped with up to eight distinct phase shifters, were reported more recently [157,158]. In these devices, the dynamic components were employed to tune the interferometer operation and to implement different phases in the three arms (see Fig.…”

Bayesian Quantum Multiphase Estimation Algorithm

“…Besides tailored postprocessing techniques [31,32], existing multiphase estimation algorithms follow a sequential scheme where an ancilla qubit encodes a single parameter at a time and is then measured. However, there is an urgent demand of parallel techniques for multiphase estimation [33][34][35][36][37][38][39][40][41][42], where different phases are estimated simultaneously [43][44][45]. Indeed, several problems of interest involve the joint estimation of multiple parameters and/or their linear combinations.…”