Abstract: A machine learning method for model-free inference of target physical parameters from a metrology dataset is generally disclosed. The disclosed method is particularly applied to atomic interferometry for sensing/measuring physical quantities such as acceleration and rotations from measured atomic interference patterns. The method operates without a need for an exact measurement-dependent mathematical/analytical model and without a need for explicit knowledge of instrumental error processes that affect the measurement. The disclosed method is based on neural networks that are trained or calibrated to learn to simultaneously estimate the target physical quantities of interest and their measurement uncertainties. It extends the applicability of a metrology when instrumental precision is limited, and noise and imperfections are present.

Abstract: A method for detecting a two-qubit correlated dephasing error includes accessing a signal of a quantum system, where the quantum system includes a plurality of qubits. Every qubit has a nonzero rate of dephasing and some qubits have a nonzero rate of correlated dephasing. The signal further includes information about a matrix that includes diagonal elements and off-diagonal elements. The off-diagonal elements of the matrix are 2 s-sparse. The method further includes performing randomized measurements of the off-diagonal elements of the matrix and recovering the matrix based on a direct measurement of the diagonal elements of the matrix.