相关论文: Topological Quantum Computing and the Jones Polyno…

In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple…

We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…

This paper reveals a conceptually new connection from information theory to approximation theory via quantum algorithms for entropy estimation. Specifically, we provide an information-theoretic lower bound $\Omega(\sqrt{n})$ on the…

Let $p$ be an odd prime number. We propose an algorithm for computing rational representations of isogenies between Jacobians of hyperelliptic curves via-adic differential equations with a sharp analysis of the loss of precision.…

The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer.…

A new algorithm for minimization of quantum cost of quantum circuits has been designed. The quantum cost of different quantum circuits of particular interest (eg. circuits for EPR, quantum teleportation, shor code and different quantum…

In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{\'e}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of…

In this paper we discuss progress made in the study of the Jones polynomial from the point of view of quantum mechanics. This study reduces to the understanding of the quantization of the moduli space of flat SU(2)-connections on a surface…

We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM…

Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…

The quantum approximate optimization algorithm (QAOA) is a promising quantum algorithm that can be used to approximately solve combinatorial optimization problems. The usual QAOA ansatz consists of an alternating application of the cost and…

Quantum $k$-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to…

Since the Jones polynomial was discovered, the connection between knot theory and quantum physics has been of great interest. Lomonaco and Kauffman introduced the knot mosaic system to give a definition of the quantum knot system that is…

Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an…

We give two quantum algorithms for computing (twisted) Kloosterman sums attached to a finite field $\mathbf{F}$ of $q$ elements. The first algorithm computes a quantum state containing, as its coefficients with respect to the standard…

Topological quantum matter represents a flexible playground to engineer unconventional excitations. While non-interacting topological single-particle systems have been studied in detail, topology in quantum many-body systems remains an open…

We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible…

We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of…

We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…