Related papers: Stochastic Estimation with $Z_2$ Noise
Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers…
We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…
We investigate the problem of estimating a given real symmetric signal matrix $\textbf{C}$ from a noisy observation matrix $\textbf{M}$ in the limit of large dimension. We consider the case where the noisy measurement $\textbf{M}$ comes…
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…
In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
In a recent paper, de Forcrand has pointed out that matrix inversions using Gaussian noise need not be iterated to full convergence, but instead may be solved approximately and treated as a heatbath. Gaussian noise however is not optimal…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
Stochastic resonance describes the utility of noise in improving the detectability of weak signals in certain types of systems. It has been observed widely in natural and engineered settings, but its utility in image classification with…
In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to…
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
$Z(2)$ lattice gauge theory plays an important role in the study of the threshold probability of Quantum Error Correction (QEC) for a quantum code. For certain QEC codes, such as the well-known Kitaev's toric/surface code, one can find a…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…
In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors,…
Quantum advantage requires overcoming noise-induced degradation of quantum systems. Conventional methods for reducing noise such as error mitigation face scalability issues in deep circuits. Specifically, noise hampers the extraction of…
We study the effects of quantum noise in hybrid quantum-classical solver for sparse systems of linear equations using quantum random walks, applied to stoquastic Hamiltonian matrices. In an ideal noiseless quantum computer, sparse matrices…
We present a new trace estimator of the matrix whose explicit form is not given but its matrix multiplication to a vector is available. The form of the estimator is similar to the Hutchison stochastic trace estimator, but instead of the…