Linear Ascending Metrological Algorithm

Abstract

Here, we devise a simple and practical protocol for qudits -LAMA -allowing to appreciably enhance the efficiency of the measurement over the standard Fourier-transform-and Kitaev algorithms. Distinct from the latter, our protocol benefits from a maximum average spin component perpendicular to the field and takes advantage from a linear step-wise increase of the Ramsey delay-time interval. Throughout our analysis, the operation of the different metrological algorithms will be addressed in the context of their qutrit [24,25] (base-3) transmon realization, as, unlike the example of a qubit (base-2) realization, this allows us to demonstrate the new algorithm's full potential. II. GENERAL PHASE-SENSITIVE PROTOCOLWe begin with a description of the general base-d phasesensitive metrological procedure employing a sequential strategy, with each step following the Preparation-Exposure-Readout (PER) logic. The procedure is aimed at the measurement of a constant magnetic field H. We work with the computational basis states |0 , |1 , . . . |d − 1 corresponding to different magnetic components M d Z with respect to the field direction (Z-axis): for instance, in the qutrit case, the basis vectors |0 , |1 , and |2 correspond, respectively, to M 3 Z =−µ, 0, +µ, where µ denotes the magnetic moment of the artificial atom [8], which serves as a coupling constant and which is known a priori. The ith step of the general procedure involves a Ramsey interference with delay time t i and is described as follows:P The qudit is prepared in a defined initial state |ψ 0 (i) ; this is experimentally realized by applying a suitable rf-pulse to the qudit ground-state [9].