Related papers: New robust ScaLAPACK routine for computing the QR …
Quantum computing promises enabling solving large problem instances, e.g. large linear equation systems with HHL algorithm, once the hardware stack matures. For the foreseeable future quantum computing will remain in the so-called NISQ era,…
We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation,…
Uncertainty Quantification (UQ) is crucial for deploying reliable Deep Learning (DL) models in high-stakes applications. Recently, General Type-2 Fuzzy Logic Systems (GT2-FLSs) have been proven to be effective for UQ, offering Prediction…
Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear…
Quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era presents significant challenges in differentiating quantum software bugs from hardware noise. Traditional debugging techniques from classical software engineering cannot…
The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…
Combining the modified matrix-vector equation approach with the technique of Lyapunov majorant function and the Banach fixed point principle, we obtain new rigorous perturbation bounds for the LU and QR factorizations with normwise or…
In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We present a formulation of the QMSTP as a mixed-integer semidefinite program…
Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed…
Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…
Using archival data from the Rossi X-ray Timing Explorer (RXTE), we study in a systematic way the variation of the quality factor and amplitude of the lower and upper kHz quasi-periodic oscillations (QPO) in the low-mass X-ray binary…
The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is…
Quantum Phase Estimation (QPE) routines are known to fail probabilistically even with perfect gates and input states. This effect stems from an incompatibility of finite-sized quantum registers to capture a phase within QPE with phase…
Recently, the graph-accelerated non-intrusive polynomial chaos (NIPC) method has been proposed for solving uncertainty quantification (UQ) problems. This method leverages the full-grid integration-based NIPC method to address UQ problems…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…
Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…
Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large…