Related papers: Improved Gaussian Approximation
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
Boson sampling is a key candidate for demonstrating quantum advantage, and has already yielded significant advances in quantum simulation, machine learning, and graph theory. In this work, a unification and extension of distinct forms of…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
Combining an optimized expansion scheme in the spirit of the background field method with the Coleman's normal-ordering renormalization prescription, we calculate the effective potential of sine-Gordon field theory beyond the Gaussian…
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…
Quantum loops in the Resonance Chiral Theory are needed to improve the implementation of non-perturbative QCD. Furthermore, the one-loop computations can predict chiral low-energy couplings at next-to-leading order, a very appealing task.…
Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
This paper presents a novel systematic methodology to obtain new simple and tight approximations, lower bounds, and upper bounds for the Gaussian Q-function, and functions thereof, in the form of a weighted sum of exponential functions.…
A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
Large-N field systems are considered from an unusual point of view. The Hamiltonian is presented in a third-quantized form analogously to the second-quantized formulation of the quantum theory of many particles. The semiclassical…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
We propose efficient classical algorithms which (strongly) simulate the action of bosonic linear optics circuits applied to superpositions of Gaussian states. Our approach relies on an augmented covariance matrix formalism to keep track of…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…