Related papers: Quantile-Based Randomized Kaczmarz for Corrupted T…
Quantum state tomography (QST) is plagued by the ``curse of dimensionality'' due to the exponentially-scaled complexity in measurement and data post-processing. Efficient QST schemes for large-scale mixed states are currently missing. In…
Accurately estimating the properties of quantum systems is a central challenge in quantum computing and quantum information. We propose a method to obtain unbiased estimators of multiple observables with low statistical error by…
Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
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…
The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…
Tensor data often suffer from missing value problem due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been proposed, most of which…
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…
Motivated by applications to covert quantum radar, we analyze a covert quantum sensing problem, in which a legitimate user aims at estimating an unknown parameter taking finitely many values by probing a quantum channel while remaining…
We propose two new algebraic reconstruction techniques based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. Tomography problems exhibit semi-convergence when iterative methods are employed, and the…
Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies: The effort of quantum tomography---the characterization of processes and states within a quantum…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
Tomographic imaging is useful for revealing the internal structure of a 3D sample. Classical reconstruction methods treat the object of interest as a vector to estimate its value. Such an approach, however, can be inefficient in analyzing…
Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…
The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…
In this article, we investigate the problem of state reconstruction of four-level quantum systems. A realistic scenario is considered with measurement results distorted by random unitary operators. Two frames which define injective…
Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A…
We investigate the randomized Kaczmarz method that adaptively updates the stepsize using readily available information for solving inconsistent linear systems. A novel geometric interpretation is provided which shows that the proposed…
We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely-positive process with no a priori information about the process apart from the dimension of the system on which the process…