Related papers: Constant-time Quantum Algorithm for Homology Detec…
The strict globular $\omega$-categories formalize the execution paths of a parallel automaton and the homotopies between them. One associates to such (and any) $\omega$-category $\C$ three homology theories. The first one is called the…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
We present a new technique for efficiently removing almost all short cycles in a graph without unintentionally removing its triangles. Consequently, triangle finding problems do not become easy even in almost $k$-cycle free graphs, for any…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous…
In this paper we consider the problem of testing whether two finite groups are isomorphic. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
In this work a loop quantum corrected model is obtained for spherically symmetric space-times in the vacuum. This effective model is derived by the use of the path integral method, previously employed in several models of Loop Quantum…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
We introduce a construction and an algorithm, both based on Topological Data Analysis (TDA), to tackle the problem of the isomorphism check of Orthogonal Arrays (OAs). Specifically, we associate to any binary OA a persistence diagram, one…
We analyze how the presence of closed timelike curves (CTCs) characterizing a time machine can be discerned by placing a local particle detector in a region of spacetime which is causally disconnected from the CTCs. Our study shows that not…
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this…
In this paper, we study the problem of computing a homotopy from a planar curve $C$ to a point that minimizes the area swept. The existence of such a minimum homotopy is a direct result of the solution of Plateau's problem. Chambers and…
The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
This paper presents a loop closure method to correct the long-term drift in LiDAR odometry and mapping (LOAM). Our proposed method computes the 2D histogram of keyframes, a local map patch, and uses the normalized cross-correlation of the…