Related papers: Error estimation in the direct state tomography
The Straight-Through (ST) estimator is a widely used technique for back-propagating gradients through discrete random variables. However, this effective method lacks theoretical justification. In this paper, we show that ST can be…
Quantum State Tomography (QST) is a fundamental technique in Quantum Information Processing (QIP) for reconstructing unknown quantum states. However, the conventional QST methods are limited by the number of measurements required, which…
We propose an estimation method for quantum measurement tomography (QMT) based on semidefinite programming (SDP), and discuss how it may be employed to detect experimental imperfections, such as shot noise and/or faulty preparation of the…
Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to…
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…
In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…
This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized…
Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a…
We investigate quantum state tomography (QST) for pure states and quantum process tomography (QPT) for unitary channels via $adaptive$ measurements. For a quantum system with a $d$-dimensional Hilbert space, we first propose an adaptive…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal…
In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…
The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making based on attribute values of objects, we shall select an…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
Inverse transport theory concerns the reconstruction of the absorption and scattering coefficients in a transport equation from knowledge of the albedo operator, which models all possible boundary measurements. Uniqueness and stability…
This work presents a distributed method for control centers to monitor the operating condition of a power network, i.e., to estimate the network state, and to ultimately determine the occurrence of threatening situations. State estimation…
State estimation (SE) of distribution networks heavily relies on pseudo measurements that introduce significant errors, since real-time measurements are insufficient. Interval SE models are regularly used, where true values of system states…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…