Related papers: Quantum Tomographic Reconstruction with Error Bars…
Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic…
The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density…
The widely-used Extended Kalman Filter (EKF) provides a straightforward recipe to estimate the mean and covariance of the state given all past measurements in a causal and recursive fashion. For a wide variety of applications, the EKF is…
Most nonlinear filters used in spacecraft navigation are based on a linear approximation of the optimal minimum mean square error estimator. The Unscented Kalman Filter (UKF) handles nonlinear dynamics through a sigma-point transform, but…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
Quantum tomography is a method to experimentally extract all that is observable about a quantum mechanical system. We introduce quantum tomography to collider physics with the illustration of the angular distribution of lepton pairs. The…
We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only $O(d)$…
Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
We present a new method for quantum process tomography. The method enables us to efficiently estimate, with fixed precision, any of the parameters characterizing a quantum channel. It is selective since one can choose to estimate the value…
We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a…
Nonlinear extensions of the Kalman filter (KF), such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are indispensable for state estimation in complex dynamical systems, yet the conditions for a nonlinear KF to…
A prime goal of quantum tomography is to provide quantitatively rigorous characterisation of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in…
We present a novel approach to transcranial ultrasound computed tomography that utilizes normalizing flows to improve the speed of imaging and provide Bayesian uncertainty quantification. Our method combines physics-informed methods and…
Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…
Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes…