Related papers: On General Lattice Quantization Noise

Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is to minimize a quadratic cost function in the state variables and…

We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux…

Propagation of unsteady waves under the effect of a step point load on a square lattice of spring-connected masses is investigated. The problem is solved by two methods. Asymptotic solutions at large time intervals, which describe the…

Simulating thimble regularization of lattice field theory can be tricky when more than one thimble is to be taken into account. A couple of years ago we proposed a solution for this problem. More recently this solution proved to be…

Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…

I discuss a new approach to constructing lattices for gauge theories with extended supersymmetry. The lattice theories themselves respect certain supersymmetries, which in many cases allows the target theory to be obtained in the continuum…

This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…

Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…

We propose a novel way to communicate signals in the form of waves across a d - dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to…

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the…

We present an experimental study of the propagation of quantum noise in a multiple scattering random medium. Both static and dynamic scattering measurements are performed: the total transmission of noise is related to the mean free path for…

It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence that challenges this consensus. Through…

The status of lattice calculations in Quantum Field Theory is reviewed. A major part is devoted to recent progress in formulating exact chiral symmetry on the lattice. Another topic which has received a lot of attention is the influence of…

This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of…

We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…

We discuss the correlation properties of current carrying states of one-dimensional insulators, which could be realized by applying an impulse to atoms loaded onto an optical lattice. While the equilibrium noise has a gapped spectrum, the…

We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse CDF. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a…