Related papers: Exact numerical simulation of power-law noises
We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization…
Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime ($10^{-7}$ Hz -- $10^{-9}$ Hz), we expect that a superposition of gravitational waves from many…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation)…
This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…
We develop and analyze a numerical method for stochastic time-fractional diffusion driven by additive fractionally integrated Gaussian noise. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative of order…
This paper studies the problem of exact localization of sparse (point or extended) objects with noisy data. The crux of the proposed approach consists of random illumination. Several recovery methods are analyzed: the Lasso, BPDN and the…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…
This paper calculates the exact quadratic variation in space and quartic variation in time for the solutions to a one dimensional stochastic heat equation driven by a multiplicative space-time white noise.
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA (low weight efficient simulation…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The…
Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
In this article, based on some simple and reasonable assumptions, we derive a Gaussian noise model for quantum amplitude estimation. We provide results from quantum amplitude estimation run on various IBM superconducting quantum computers…
We present a method designed to estimate the noise power spectrum in the time domain for CMB experiments. The noise power spectrum is extracted from the time ordered data avoiding the contamination coming from sky signal and accounting the…
As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is…