相关论文: QuantileRK: Solving Large-Scale Linear Systems wit…

We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…

In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…

Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…

By introducing a subsampling strategy, we propose a randomized block Kaczmarz-Motzkin method for solving linear systems. Such strategy not only determines the block size, but also combines and extends two famous strategies, i.e., randomness…

In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework,…

Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…

Scalable quantum computing can become a reality with error correction, provided coherent qubits can be constructed in large arrays. The key premise is that physical errors can remain both small and sufficiently uncorrelated as devices…

Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when…

We study the problem of robust estimation under heterogeneous corruption rates, where each sample may be independently corrupted with a known but non-identical probability. This setting arises naturally in distributed and federated…

Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…

Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to…

To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be…

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…

Quantum Error Mitigation is essential for enhancing the reliability of quantum computing experiments. The adaptive KIK error mitigation method has demonstrated significant advantages, including resilience to temporal noise drifts,…

We investigate machine learning based on clustering techniques that are suitable for the detection of encoded strings of q-ary symbols transmitted over a noisy channel with partially unknown characteristics. We consider the detection of the…

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging,…

We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal…

Solving under-determined systems of linear equations with sparse solutions attracted enormous amount of attention in recent years, above all, due to work of \cite{CRT,CanRomTao06,DonohoPol}. In \cite{CRT,CanRomTao06,DonohoPol} it was…