Related papers: An algorithm for computing the canonical bases of …
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on four sub-classes: (1) When all coefficients are integers…
Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the…
This paper investigates learning-augmented algorithms for smooth integer programs, covering canonical problems such as MAX-CUT and MAX-k-SAT. We introduce a framework that incorporates a predictive oracle to construct a linear surrogate of…
We introduce a $q$-deformation of the Fock space of holomorphic functions on $\mathbb{C}$, based on a geometric definition of $q$-analyticity. This definition is inspired by a standard construction in complex differential geometry. Within…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
In this paper, we obtain affine analogues of Gindikin-Karpelevich formula and Casselman-Shalika formula as sums over Kashiwara-Lusztig's canonical bases. Suggested by these formulas, we define natural $q$-deformation of arithmetical…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
We construct a canonical basis for quantum generalized Kac-Moody algebra via semisimple perverse sheaves on varieties of representations of quivers. We compare this basis with the one recently defined purely algebraically by Jeong, Kang and…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…