相关论文: Improved Gaussian Approximation
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
We review existing classical simulation methods for performing fermionic Gaussian operations and develop new methods to address the gap by adhering to the fundamental theoretical framework established by Bravyi [Quantum Info. Comput. 5, 216…
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…
The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
A systematic replica field theory calculations are analysed using the examples of two particular one-dimensional "toy" random models with Gaussian disorder. Due to apparent simplicity of the model the replica trick calculations can be…
We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We…
This paper is an overview of the classical level crossing problem which is studied extensively in the literature and is fundamental in many branches of applied probability. We discuss a number of approximations with an emphasis on their…
This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…
We have considered phi^4 theory in higher dimensions. Using functional diagrammatic approach, we computed the one-loop correction to effective potential of the scalar field in five dimensions. It is shown that phi^4 theory can be…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
This is a collection of various result and notes, addressing the sum-of-squares hierarchy for spin and fermion systems using some ideas from quantum field theory, including higher order perturbation theory, critical phenomena, nonlocal…
We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a…