Related papers: Notes on color reductions and $\gamma$ traces

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and…

After a brief introduction to the problem of subtraction of infrared divergences for high-order collider observables, we present a preliminary study of strongly-ordered soft and collinear multiple radiation from the point of view of…

This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on…

Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a…

Here I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to simplify the…

The paper establishes the new state-of-art in the accuracy analysis of Hutchinson's trace estimator. Leveraging tools that have not been previously used in this context, particularly hypercontractive inequalities and concentration…

In this paper, we prove results on the relationship between the complexity of the group and color isomorphism problems. The difficulty of color isomorphism problems is known to be closely linked to the the composition factors of the…

Graph workloads pose a particularly challenging problem for query optimizers. They typically feature large queries made up of entirely many-to-many joins with complex correlations. This puts significant stress on traditional cardinality…

We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.

In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…

We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…

Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use the flexibility inherent in this…

Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…

In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…

This paper collects miscellaneous results about the group SU(1,1) that are helpful in applications in quantum optics. Moreover, we derive two new results, the first is about the approximability of SU(1,1) elements by a finite set of…

Some algorithms for the numerically exact treatment of fermion determinants are summarised. This is not supposed to be a review, rather a concise handbook. The audience is expected to have a basic understanding of how to put fermions on a…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…

For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma is colorable from an assignment of lists of size three in time O(|V(G)|). Furthermore, we can allow a subgraph…

Path integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to $SU(N)$ lattice gauge…